{"id":25367,"date":"2020-12-22T10:14:36","date_gmt":"2020-12-22T10:14:36","guid":{"rendered":"https:\/\/tnboardsolutions.com\/?p=25367"},"modified":"2021-07-08T01:57:27","modified_gmt":"2021-07-08T07:27:27","slug":"samacheer-kalvi-11th-maths-guide-chapter-8-ex-8-5","status":"publish","type":"post","link":"https:\/\/tnboardsolutions.com\/samacheer-kalvi-11th-maths-guide-chapter-8-ex-8-5\/","title":{"rendered":"Samacheer Kalvi 11th Maths Guide Chapter 8 Vector Algebra – I Ex 8.5"},"content":{"rendered":"

Tamilnadu State Board New Syllabus\u00a0Samacheer Kalvi 11th Maths Guide<\/a> Pdf Chapter 8 Vector Algebra – I Ex 8.5 Text Book Back Questions and Answers, Notes.<\/p>\n

Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 8 Vector Algebra – I Ex 8.5<\/h2>\n

Choose the correct or the most suitable answer from the given four alternatives:<\/p>\n

Question 1.
\nThe value of \\(\\overrightarrow{\\mathbf{A B}}+\\overrightarrow{\\mathbf{B C}}+\\overrightarrow{\\mathbf{D A}}+\\overrightarrow{\\mathbf{C D}}\\) is
\n(1) \\(\\overrightarrow{\\mathbf{A D}}\\)
\n(2) \\(\\overrightarrow{\\mathbf{C A}}\\)
\n(3) \\(\\overrightarrow{0}\\)
\n(4) \\(-\\overrightarrow{\\mathbf{A D}}\\)
\nAnswer:
\n(3) \\(\\overrightarrow{0}\\)<\/p>\n

Explaination:
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 2.
\nIf \\(\\overrightarrow{\\mathbf{a}}+2 \\overrightarrow{\\mathbf{b}}\\) and \\(3 \\overrightarrow{\\mathbf{a}}+\\mathbf{m} \\overrightarrow{\\mathbf{b}}\\) are parallel, then the value of m is
\n(1) 3
\n(2) \\(\\frac{1}{3}\\)
\n(3) 6
\n(4) \\(\\frac{1}{6}\\)
\nAnswer:
\n(3) 6<\/p>\n

Explaination:
\n\"Samacheer<\/p>\n

Question 3.
\nThe unit vector parallel to the resultant of the vectors i\u0302 + j\u0302 – k\u0302 and i\u0302 – 2j\u0302 + k\u0302 is
\n(1) \"Samacheer
\n(2)\"Samacheer
\n(3) \"Samacheer
\n(4) \"Samacheer
\nAnswer:
\n(4) \"Samacheer<\/p>\n

Explaination:
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 4.
\nA vector \\(\\overrightarrow{\\mathbf{O P}}\\) makes 60\u00b0 and 45\u00b0 with the positive direction of the x and y axes respectively. Then the angle between \\(\\overrightarrow{\\mathbf{O P}}\\) and the z – axis is
\n(1) 45\u00b0
\n(2) 60\u00b0
\n(3) 90\u00b0
\n(4) 30\u00b0
\nAnswer:
\n(2) 60\u00b0<\/p>\n

Explaination:
\nGiven the angle made by \\(\\overrightarrow{\\mathbf{O P}}\\) with x – axis and y – axis are 60\u00b0 and 45\u00b0 respectively. Let the angle made by \\(\\overrightarrow{\\mathbf{O P}}\\) with the positive direction of z – axis be \u03b8. Then
\n\"Samacheer<\/p>\n

Question 5.
\nIf \\(\\overrightarrow{\\mathbf{B A}}\\) = 3i\u0302 + 2j\u0302 + k\u0302 and the position vector of B is i\u0302 + 3j\u0302 – k\u0302 then the position vector A is
\n(1) 4i\u0302 + 2j\u0302 + k\u0302
\n(2) 4i\u0302 + 5j\u0302
\n(3) 4i\u0302
\n(4) – 4i\u0302
\nAnswer:
\n(2) 4i\u0302 + 5j\u0302<\/p>\n

Explaination:
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 6.
\nA vector makes equal angle with the positive direction of the coordinate axes . Then each angle is equal to
\n(1) cos-1<\/sup>\\(\\left(\\frac{1}{3}\\right)\\)
\n(2) cos-1<\/sup>\\(\\left(\\frac{2}{3}\\right)\\)
\n(3) cos-1<\/sup>\\(\\left(\\frac{1}{\\sqrt{3}}\\right)\\)
\n(4) cos-1<\/sup>\\(\\left(\\frac{2}{\\sqrt{3}}\\right)\\)
\nAnswer:
\n(3) cos-1<\/sup>\\(\\left(\\frac{1}{\\sqrt{3}}\\right)\\)<\/p>\n

Explaination:
\nLet the angles made by a vector with the coordinate axes be \u03b1, \u03b1, \u03b1. Then
\ncos2<\/sup> \u03b1 + cos2<\/sup> \u03b1 + cos2<\/sup> \u03b1 = 1
\n[If \u03b1, \u03b2, \u03b3 are the angles made by a vector with coordinate axes respectively, then
\ncos2<\/sup> \u03b1 + cos2<\/sup> \u03b2 + cos2<\/sup> \u03b3 = 1]
\n3 cos2<\/sup> \u03b1 = 1
\n\"Samacheer<\/p>\n

Question 7.
\nThe vector \\(\\overrightarrow{\\mathbf{a}}-\\overrightarrow{\\mathbf{b}}, \\overrightarrow{\\mathbf{b}}-\\overrightarrow{\\mathbf{c}}, \\overrightarrow{\\mathbf{c}}-\\overrightarrow{\\mathbf{a}}\\) are
\n(1) parallel to each other
\n(2) unit vectors
\n(3) mutually perpendicular vectors
\n(4) coplanar vectors
\nAnswer:
\n(4) coplanar vectors<\/p>\n

Explaination:
\n\"Samacheer
\n[The condition for the three vectors \\(\\vec{a}\\), \\(\\vec{b}\\), \\(\\vec{c}\\) to be coplanar is \\(\\vec{a}\\) = \u03bb\\(\\vec{a}\\) + \u03bc\\(\\vec{b}\\) where \u03bb, \u03bc are scalars. That is one vector is a Linear combination of the other two vectors.]
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 8.
\nIf ABCD is a parallelogram, then \\(\\overrightarrow{\\mathbf{A B}}+\\overrightarrow{\\mathbf{A D}}+\\overrightarrow{\\mathbf{C B}}+\\overrightarrow{\\mathbf{C D}}\\) is equal to
\n(1) 2 \\((\\overrightarrow{\\mathbf{A B}}+\\overrightarrow{\\mathbf{A D}})\\)
\n(2) 4 \\(\\overrightarrow{\\mathbf{A C}}\\)
\n(3) 4 \\(\\overrightarrow{\\mathbf{B D}}\\)
\n(4) \\(\\overrightarrow{0}\\)
\nAnswer:
\n(4) \\(\\overrightarrow{0}\\)<\/p>\n

Explaination:
\n\"Samacheer<\/p>\n

Question 9.
\nOne of the diagonals of parallelogram ABCD with \\(\\vec{a}\\) and \\(\\vec{b}\\) as adjacent sides is \\(\\vec{a}\\) + \\(\\vec{b}\\). The other diagonal BD is
\n(1) \\(\\vec{a}\\) – \\(\\vec{b}\\)
\n(2) \\(\\vec{b}\\) – \\(\\vec{a}\\)
\n(3) \\(\\vec{a}\\) + \\(\\vec{b}\\)
\n(4) \\(\\frac{\\overrightarrow{\\mathbf{a}}+\\overrightarrow{\\mathbf{b}}}{2}\\)
\nAnswer:
\n(2) \\(\\vec{b}\\) – \\(\\vec{a}\\)<\/p>\n

Explaination:
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 10.
\nIf \\(\\vec{a}\\), \\(\\vec{b}\\) are the vectors A and B, then which one o the following points whose position vector lies on AB, is
\n(1) \\(\\vec{a}\\) + \\(\\vec{b}\\)
\n(2) \\(\\frac{2 \\vec{a}-\\vec{b}}{2}\\)
\n(3) \\(\\frac{2 \\vec{a}+\\vec{b}}{3}\\)
\n(4) \\(\\frac{\\vec{a}-\\vec{b}}{3}\\)
\nAnswer:
\n(3) \\(\\frac{2 \\vec{a}+\\vec{b}}{3}\\)<\/p>\n

Explaination:
\n\"Samacheer<\/p>\n

Question 11.
\nIf \\(\\vec{a}\\), \\(\\vec{b}\\), \\(\\vec{c}\\) are the position vectors of three collinear points, then which of the following is true?
\n(1) \\(\\overrightarrow{\\mathbf{a}}=\\overrightarrow{\\mathbf{b}}+\\overrightarrow{\\mathbf{c}}\\)
\n(2) \\(2 \\overrightarrow{\\mathbf{a}}=\\overrightarrow{\\mathbf{b}}+\\overrightarrow{\\mathbf{c}}\\)
\n(3) \\(\\overrightarrow{\\mathbf{b}}=\\overrightarrow{\\mathbf{c}}+\\overrightarrow{\\mathbf{a}}\\)
\n(4) \\(4 \\overrightarrow{\\mathbf{a}}+\\overrightarrow{\\mathbf{b}}+\\overrightarrow{\\mathbf{c}}=0\\)
\nAnswer:
\n(2) \\(2 \\overrightarrow{\\mathbf{a}}=\\overrightarrow{\\mathbf{b}}+\\overrightarrow{\\mathbf{c}}\\)<\/p>\n

Explaination:
\n\"Samacheer
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 12.
\nIf \\(\\vec{r}\\) = \\(\\frac{9 \\vec{a}+7 \\vec{b}}{16}\\), then the point p whose position vector \\(\\vec{r}\\) divides the line joining the points with position vectors \\(\\vec{a}\\) and \\(\\vec{b}\\) in the ratio
\n(1) 7 : 9 internally
\n(2) 9 : 7 internally
\n(3) 9 : 7 externally
\n(4) 7 : 9 externally
\nAnswer:
\n(1) 7 : 9 internally<\/p>\n

Explaination:
\n\"Samacheer
\n\"Samacheer<\/p>\n

Question 13.
\nIf \u03bbi\u0302 + 2\u03bbj\u0302 + 2\u03bbk\u0302 is a unit vector, then the value of \u03bb is
\n(1) \\(\\frac{1}{3}\\)
\n(2) \\(\\frac{1}{4}\\)
\n(3) \\(\\frac{1}{9}\\)
\n(4) \\(\\frac{1}{2}\\)
\nAnswer:
\n(1) \\(\\frac{1}{3}\\)<\/p>\n

Explaination:
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 14.
\nTwo vertices of a triangle have position vectors 3i\u0302 + 4j\u0302 – 4k\u0302 and 2i\u0302 + 3j\u0302 + 4k\u0302. If the position vector of the centroid is i\u0302 + 2j\u0302 + 3k\u0302, then the position vector of the third vertex is
\n(1) – 2i\u0302 – j\u0302 + 9k\u0302
\n(2) – 2i\u0302 – j\u0302 – 6k\u0302
\n(3) 2i\u0302 – j\u0302 + 6k\u0302
\n(4) – 2i\u0302 + j\u0302 + 6k\u0302
\nAnswer:
\n(1) – 2i\u0302 – j\u0302 + 9k\u0302<\/p>\n

Explaination:
\nLet ABC be a triangle with centroid G. Given that
\n\"Samacheer
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 15.
\n\"Samacheer
\n(1) 42
\n(2) 12
\n(3) 22
\n(4) 32
\nAnswer:
\n(3) 22<\/p>\n

Explaination:
\n\"Samacheer
\n\"Samacheer<\/p>\n

Question 16.
\nIf \\(\\vec{a}\\) and \\(\\vec{b}\\) having same magnitude and angle between them is 60\u00b0 and their scalar product \\(\\frac{1}{2}\\) is then |\\(\\vec{a}\\)| is
\n(1) 2
\n(2) 3
\n(3) 7
\n(4) 1
\nAnswer:
\n(4) 1<\/p>\n

Explaination:
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 17.
\nThe value of \u03b8 \u2208 (0, \\(\\frac{\\pi}{2}\\)) for which the vectors \\(\\vec{a}\\) = (sin \u03b8) i\u0302 + (cos \u03b8) j\u0302 and \\(\\vec{b}\\) = i\u0302 – \u221a3j\u0302 + 2k\u0302 are perpendicular is equal to
\n(1) \\(\\frac{\\pi}{3}\\)
\n(2) \\(\\frac{\\pi}{6}\\)
\n(3) \\(\\frac{\\pi}{4}\\)
\n(4) \\(\\frac{\\pi}{2}\\)
\nAnswer:
\n(1) \\(\\frac{\\pi}{3}\\)<\/p>\n

Explaination:
\n\"Samacheer<\/p>\n

Question 18.
\n\"Samacheer
\n(1) 15
\n(2) 35
\n(3) 45
\n(4) 25
\nAnswer:
\n(4) 25<\/p>\n

Explaination:
\n\"Samacheer
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 19.
\n\"Samacheer
\n(1) 225
\n(2) 275
\n(3) 325
\n(4) 300
\nAnswer:
\n(4) 300<\/p>\n

Explaination:
\n\"Samacheer
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 20.
\nIf \\(\\vec{a}\\) and \\(\\vec{b}\\) are two vectors of magnitude 2 and inclined at an angle 60\u00b0, then the angle between \\(\\vec{a}\\) and \\(\\vec{a}\\) + \\(\\vec{b}\\) is
\n(1) 30\u00b0
\n(2) 60\u00b0
\n(3) 45\u00b0
\n(4) 90\u00b0
\nAnswer:
\n(1) 30\u00b0<\/p>\n

Explaination:
\n\"Samacheer
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 21.
\nIf the projection of 5i\u0302 – j\u0302 – 3k\u0302 on the vector i\u0302 + 3j\u0302 + \u03bbk\u0302 is same as the projection of i\u0302 + 3j\u0302 + \u03bbk\u0302 on 5i\u0302 – j\u0302 – 3k\u0302, then \u03bb is equal to
\n(1) \u00b1 4
\n(2) \u00b1 3
\n(3) \u00b1 5
\n(4) \u00b1 1
\nAnswer:
\n(3) \u00b1 5<\/p>\n

Explaination:
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 22.
\nIf (1, 2, 4) and (2, – 3\u03bb – 3) are the initial and terminal points of the vector i\u0302 + 5j\u0302 – 7k\u0302 then the value of \u03bb is equal to
\n(1) \\(\\frac{7}{3}\\)
\n(2) \\(-\\frac{7}{3}\\)
\n(3) \\(-\\frac{5}{3}\\)
\n(4) \\(\\frac{7}{3}\\)
\nAnswer:
\n(4) \\(\\frac{7}{3}\\)<\/p>\n

Explaination:
\n\"Samacheer
\n\"Samacheer
\nEquating the like terms
\n5 = – 3\u03bb – 2
\n3\u03bb = – 5 – 2 = – 7
\n\u03bb = \\(-\\frac{7}{3}\\)<\/p>\n

\"Samacheer<\/p>\n

Question 23.
\nIf the points whose position vectors 10i\u0302 + 3j\u0302, 12i\u0302 – 5j\u0302 and ai\u0302 + 11j\u0302 are collinear then a is equal to
\n(1) 6
\n(2) 3
\n(3) 5
\n(4) 8
\nAnswer:
\n(4) 8<\/p>\n

Explaination:
\nThe position vectors of the three points are
\n\"Samacheer
\nThe condition for the three points A, B, C are collinear is the area of the triangle formed by these points is zero.
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 24.
\n\"Samacheer
\n(1) 5
\n(2) 7
\n(3) 26
\n(4) 10
\nAnswer:
\n(3) 26<\/p>\n

Explaination:
\n\"Samacheer
\n\"Samacheer
\n(4x + 1) – 7 – (2 + x) = 70
\n4x + 1 – 7 – 2 – x = 70
\n3x – 8 = 70
\n3x = 70 + 8
\n3x = 78
\nx = \\(\\frac{78}{3}\\) = 26<\/p>\n

\"Samacheer<\/p>\n

Question 25.
\nIf \\(\\vec{a}\\) = i\u0302 + 2j\u0302 + 2k\u0302, |\\(\\vec{b}\\)| = 5 and the angle between \\(\\vec{a}\\) and \\(\\vec{b}\\) is \\(\\frac{\\pi}{6}\\), then the area of the triangle formed by these two vectors as two sides, is
\n(1) \\(\\frac{7}{4}\\)
\n(2) \\(\\frac{15}{4}\\)
\n(3) \\(\\frac{3}{4}\\)
\n(4) \\(\\frac{17}{4}\\)
\nAnswer:
\n(2) \\(\\frac{15}{4}\\)<\/p>\n

Explaination:
\n\"Samacheer<\/p>\n","protected":false},"excerpt":{"rendered":"

Tamilnadu State Board New Syllabus\u00a0Samacheer Kalvi 11th Maths Guide Pdf Chapter 8 Vector Algebra – I Ex 8.5 Text Book Back Questions and Answers, Notes. Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 8 Vector Algebra – I Ex 8.5 Choose the correct or the most suitable answer from the given four alternatives: Question 1. The …<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/tnboardsolutions.com\/wp-json\/wp\/v2\/posts\/25367"}],"collection":[{"href":"https:\/\/tnboardsolutions.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/tnboardsolutions.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/tnboardsolutions.com\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/tnboardsolutions.com\/wp-json\/wp\/v2\/comments?post=25367"}],"version-history":[{"count":0,"href":"https:\/\/tnboardsolutions.com\/wp-json\/wp\/v2\/posts\/25367\/revisions"}],"wp:attachment":[{"href":"https:\/\/tnboardsolutions.com\/wp-json\/wp\/v2\/media?parent=25367"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/tnboardsolutions.com\/wp-json\/wp\/v2\/categories?post=25367"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/tnboardsolutions.com\/wp-json\/wp\/v2\/tags?post=25367"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}