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Question: If \(\overset{\rightarrow}{A} = 4\widehat{i} - 3\widehat{j}\) and \(\overset{\rightarrow}{B} = 6\wid...

If A→=4i^−3j^\overset{\rightarrow}{A} = 4\widehat{i} - 3\widehat{j} and B→=6i^+8j^\overset{\rightarrow}{B} = 6\widehat{i} + 8\widehat{j} then magnitude and direction of A→+B→\overset{\rightarrow}{A} + \overset{\rightarrow}{B} will be-

A

(a) 5,tan⁡−1(3/4)5,\tan^{- 1}(3/4)

A

(b) 55,tan⁡−1(1/2)5\sqrt{5},\tan^{- 1}(1/2)

A

(c) 10,tan⁡−1(5)10,\tan^{- 1}(5)

A

(d) 25,tan⁡−1(3/4)25,\tan^{- 1}(3/4)

Explanation

Solution

(b)

A→+B→=4i^−3j^+6i^+8j^=10i^+5j^\overset{\rightarrow}{A} + \overset{\rightarrow}{B} = 4\widehat{i} - 3\widehat{j} + 6\widehat{i} + 8\widehat{j} = 10\widehat{i} + 5\widehat{j}

∣A→+B→∣=(10)2+(5)2|\overset{\rightarrow}{A} + \overset{\rightarrow}{B}| = \sqrt{(10)^{2} + (5)^{2}} =55= 5\sqrt{5}

tan⁡θ=510=12\tan\theta = \frac{5}{10} = \frac{1}{2} ⇒θ=tan⁡−1(12)\Rightarrow \theta = \tan^{- 1}\left( \frac{1}{2} \right)