First slide

Scalars and Vectors

Question

If $\vec{A} = 4 \hat{i} - 3 \hat{j} and \vec{B} = 6 \hat{i} + 8 \hat{j}$ then magnitude and direction of $\vec{A} + \vec{B}$ will be

Moderate

A

$5, \tan^{- 1} (\frac{3}{4})$
B

$5 \sqrt{5}, \tan^{- 1} (\frac{1}{2})$
C

$10, \tan^{- 1} (5)$
D

$25, \tan^{- 1} (\frac{3}{4})$

Solution

$\vec{A} + \vec{B} = 4 \hat{i} - 3 \hat{j} + 6 \hat{i} + 8 \hat{j} = 10 \hat{i} + 5 \hat{j} \Rightarrow |\vec{A} + \vec{B}| = \sqrt{{(10)}^{2} + {(5)}^{2}} = 5 \sqrt{5} \Rightarrow tanθ = \frac{5}{10} = \frac{1}{2} \Rightarrow θ = \tan^{- 1} (\frac{1}{2})$

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