Question

10. Given: A = 3i - 4j –2k and B = 2î + 4 j - 5k .
The angle which A + B makes with Y-axis is
(a) 0°
(b) 45°
(c) 60°
(d) 90°​

Answer 1

Answer:

$\displaystyle{\theta=90}$

d . option is correct .

Explanation:

Given :

$\displaystyle{\vec A=3\hat{i}-4\hat{j}-2\hat{k} \ and}\\\\\\\displaystyle{\vec B=2\hat{i}+4\hat{j}-5\hat{k}}\\\\\\\displaystyle{Now }\\\\\\{\displaystyle \vec A+\vec B\implies 3\hat{i}-4\hat{j}-2\hat{k}+2\hat{i}+4\hat{j}-5\hat{k}}\\\\\\\displaystyle{\vec A+\vec B\implies\hat{i}-7\hat{k}}$

Here coefficient of j = 0

Now angle with y - axis

$\displaystyle{\cos\theta=\dfrac{y}{\sqrt{x^2+y^2+z^2}}}\\\\\\\displaystyle{\cos\theta=\dfrac{0}{\sqrt{x^2+y^2+z^2}}}\\\\\\\displaystyle{\cos \theta=0}\\\\\\\displaystyle{\cos \theta=\cos90}\\\\\\\displaystyle{\theta=90}$

Thus we get answer.