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## Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 6 Applications of Vector Algebra Ex 6.3

Question 1.

Solution:

Question 2.

For any vector \(\vec{a}\), prove that

Solution:

Question 3.

Prove that \([\vec{a}-\vec{b}, \vec{b}-\vec{c}, \vec{c}-\vec{a}]\) = 0

Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.

If \(\vec{a}, \vec{b}, \vec{c}, \vec{d}\) are coplanar vectors, show that \((\vec{a} \times \vec{b}) \times(\vec{c} \times \vec{d})=\overrightarrow{0}\)

Solution:

Question 7.

If , find the values of l, m, n

Solution:

On solving (3) & (4)

Question 8.

If \(\hat{a}, \hat{b}, \hat{c}\) are three unit vectors such that \(\hat{b} \text { and } \hat{c}\) are non-parallel and \(\hat{a} \times(\hat{b} \times \hat{c})=\frac{1}{2} \hat{b}\), find the angle between \(\hat{a}\) and \(\hat{c}\).

Solution:

### Samacheer Kalvi 12th Maths Solutions Chapter 6 Applications of Vector Algebra Ex 6.3 Additional Problems

Question 1.

If and show that they are not equal.

Solution:

Question 2.

Solution: