If A→= 4i^−3j^ and B→= 6i^+8j^ then magnitude and direction of A→+B→ from +x axis will be

A→ + B→ = 4i^−3j^+6i^+8j^= 10i^+5j^|A→+B|→ = (10)2+(5)2 = 55tanθ = 510 = 12 ⇒θ =tan-1(12)

If A→= 4i^−3j^ and B→= 6i^+8j^ then magnitude and direction of A→+B→ from +x axis will be

A→ + B→ = 4i^−3j^+6i^+8j^= 10i^+5j^|A→+B|→ = (10)2+(5)2 = 55tanθ = 510 = 12 ⇒θ =tan-1(12)

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

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

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

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

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

answer is B.

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$\vec{A} + \vec{B} = 4 \hat{i} - 3 \hat{j} + 6 \hat{i} + 8 \hat{j} = 10 \hat{i} + 5 \hat{j}$

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

$tanθ = \frac{5}{10} = \frac{1}{2} \Rightarrow θ = \tan^{- 1} (\frac{1}{2})$

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If A→= 4i^−3j^ and B→= 6i^+8j^ then magnitude and direction of A→+B→ from +x axis will be

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