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Question

Find the angle between vector P and vector Q if pā†’=qā†’&pā†’-qā†’=pā†’+qā†’


A

45Ā°

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B

90Ā°

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C

135Ā°

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D

150Ā°

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Solution

The correct option is B

90Ā°


Explanation for correct option:

Finding the angle:

Step-1: Apply formula |aā†’Ā±bā†’|2=|aā†’|2+|bā†’|2Ā±2|aā†’||bā†’|cos(Īø)

Given, pā†’=qā†’&pā†’-qā†’=pā†’+qā†’

ā‡’aā†’2+bā†’2+2aā†’bā†’cosĪø=aā†’2+bā†’2-2aā†’bā†’cosĪø

Step-2: Squaring both sides.

ā‡’aā†’2+bā†’2+2aā†’bā†’cosĪø2=aā†’2+bā†’2-2aā†’bā†’cosĪø2

ā‡’ aā†’2+bā†’2+2aā†’bā†’cosĪø=aā†’2+bā†’2-2aā†’bā†’cosĪø

ā‡’ 4aā†’bā†’cosĪø=0

ā‡’ Īø=90Ā°

Hence, correct answer is option B.


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