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Question

What is the component of (3^i+4^j) along (^i+^j)?

A
12(^j+^i)
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B
32(^j+^i)
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C
52(^j+^i)
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D
72(^j+^i)
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Solution

The correct option is D 72(^j+^i)
Step 1: Scalar projection of B along A [Ref. Fig.]
Let say, B=3^i+4^j, A=^i+^j
Magnitude of component of B along A=|B|cosθ
=A.B|A|=3+42=72 [A.B=|A||B|cosθ]
This is the magnitude of component of B along A

Step 2: Vector Projection
Component of B along A=A.B|A|^A=72×(^i+^j)2=72(^i+^j)
This is the component of B along A
Hence option D is correct.

2110179_118106_ans_73d918ccc9484fc9a35f4988f9f44fa7.png

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