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Question: If \(\vec { A } = 4 \hat { i } - 3 \hat { j }\) and \(\vec { A } + \vec { B }\) will be...

If A⃗=4i^−3j^\vec { A } = 4 \hat { i } - 3 \hat { j } and A⃗+B⃗\vec { A } + \vec { B } will be

A

5,tan⁡−1(3/4)5 , \tan ^ { - 1 } ( 3 / 4 )

B

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

C

D

25,tan⁡−1(3/4)25 , \tan ^ { - 1 } ( 3 / 4 )

Answer

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

Explanation

Solution

A⃗+B⃗=4i^−3j^+6i^+8j^=10i^+5j^\vec { A } + \vec { B } = 4 \hat { i } - 3 \hat { j } + 6 \hat { i } + 8 \hat { j } = 10 \hat { i } + 5 \hat { j }

=55= 5 \sqrt { 5 }

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