Question

10. A= 3ť – j +7k and B =si – +9ť. The direction
cosine of the vector A+B with x-axis is
3
8
(1) 131
(2)
1324
(3) 5
324
11. The angle between the two vectors
Ā=3ť +4j +5k and B = 3î +4j +5k is
(1) 60°
(2) Zero
(3) 90°
(4) None of these
12. The angle between the two vectors​

Answer 1

Question 10.

A+B $\large\rm { \implies (3 \hat{i} - \hat{j} + 7 \hat{k} ) + ( 5 \hat{i} - \hat{j} + 9 \hat{k} ) }$

$\large\rm { \implies 8 \hat{i} - 2 \hat{j} + 16 \hat{k} ) }$

Direction cosines

$\large\rm { \alpha = \frac{v_{x}}{ \sqrt { v^{2} _{x} + v^{2}_{y} + v^{2}_{z} }}}$

$\large\rm { \alpha = \frac{8}{18} = \frac{4}{9}}$

$\large\rm { \beta = \frac{-2}{18} = \frac{-1}{9}}$

$\large\rm { \gamma = \frac{16}{18} = \frac{8}{9}}$

Question 11.

$\large\rm { \vec{A} = 3 \hat{i} + 4 \hat{j} + 5 \hat{k} }$

$\large\rm { \vec{B} = 3 \hat{i} + 4 \hat{j} - 5 \hat{k} }$

$\large\rm { \cos \theta = \frac{ \vec{A} \cdot \vec{B}}{ | \vec{A} | | \vec{B} | }}$

$\large\rm { = \frac{9+16-25}{50} = 0}$

so, $\large\rm { \theta = 90}$