First slide

Vectors

Question

If $\bar{A}$ = 4 $\hat{i}$ - 2 $\hat{j}$ + 6 $\hat{k}$ , and $\bar{B}$ = $\hat{i}$ - 2 $\hat{j}$ - 3 $\hat{k}$ , the angle which the $\bar{A}$ + $\bar{B}$ makes with the x – axis is

Easy

A

$\cos^{- 1} 3 / \sqrt{50}$
B

$\cos^{- 1} 5 / \sqrt{50}$
C

$\cos^{- 1} 4 / \sqrt{50}$
D

$\cos^{- 1} 12 / \sqrt{50}$

Solution

$\begin{array}{l} \vec{A} + \vec{B} = 5 \hat{i} - 4 \hat{j} + 3 \hat{k} \\ (\vec{A} + \vec{B}) . \hat{i} = |\vec{A} + \vec{B}| . |\hat{i}| . Cos θ \\ \Rightarrow 5 = \sqrt{5^{2} + {(- 4)}^{2} + 3^{2}} .1. Cos θ \\ \Rightarrow Cos θ = \frac{5}{\sqrt{50}}, θ = {Cos}^{- 1} (\frac{5}{\sqrt{50}}) \end{array}$

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