Samacheer Kalvi 11th Maths Guide Chapter 8 Vector Algebra – I Ex 8.4

Tamilnadu State Board New Syllabus Samacheer Kalvi 11th Maths Guide Pdf Chapter 8 Vector Algebra – I Ex 8.4 Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 8 Vector Algebra – I Ex 8.4

Question 1.
Find the magnitude of \(\vec{a}\) × \(\vec{b}\) if \(\vec{a}\) = 2î + ĵ + 3k̂ and \(\vec{b}\) = 3î + 5ĵ – 2k̂
Answer:
The given vectors are \(\vec{a}\) = 2î + ĵ + 3k̂
\(\vec{b}\) = 3î + 5ĵ – 2k̂

Question 2.
Show that

Answer:

Question 3.
Find the vectors of magnitude 10√3 that are perpendicular to the plane which contains
î + 2ĵ + k̂ and î + 3ĵ + 4k̂
Answer:
Let the given vectors be \(\vec{a}\) = î + 2ĵ + k̂
\(\vec{b}\) = î + 3ĵ + 4k̂

Question 4.
Find the unit vectors perpendicular to each of the vectors \(\vec{a}\) + \(\vec{b}\) and \(\vec{a}\) – \(\vec{b}\), where \(\vec{a}\) = î + ĵ + k̂ and \(\vec{b}\) = î + 2ĵ + 3k̂
Answer:

Question 5.
Find the area of the parallelogram whose two adjacent sides are determined by the vectors î + 2ĵ + 3k̂ and 3î – 2ĵ + k̂
Answer:

Question 6.
Find the area of the triangle whose vertices are A(3, -1, 2), B(1, -1, -3), and C(4, -3, 1)
Answer:
The given vertices of the triangle ABC are
A(3, -1, 2), B(1, -1, -3) and C(4, -3, 1)

Question 7.

Answer:

Question 8.
For any vector \(\vec{a}\) prove that

Answer:

Question 9.

Answer:

Question 10.
Find the angle between the vector 2î + ĵ – k̂ and î + 2ĵ + k̂ using vector product.
Answer:
Let the given vector be \(\vec{a}\) = 2î + ĵ – k̂ and \(\vec{b}\) = 2î + ĵ – k̂