Q7 / 16 · NTA Abhyas (NEET) 2020 · Physics · Mathematics in Physics

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

A
$5, \tan^{- 1} (\frac{3}{4})$
Correct answer
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}

|\vec{A} + \vec{B}| = \sqrt{{(10)}^{2} + {(5)}^{2}} = 5 \sqrt{5}

\tan θ = \frac{5}{10} = \frac{1}{2}

\Rightarrow

θ = \tan^{- 1} (\frac{1}{2})

Hence, the correct answer is option: 'B'.

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