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Question

Let |A1|=3,|A2|=5 and |A1+A2|=5. The value of (2A1+3A2).(3A12A2) is,

A
112.5
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B
106.5
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C
99.5
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D
118.5
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Solution

The correct option is D 118.5
Using,
|A1+A2|=A21+A22+2A1A2cosθ

5=32+52+2×3×5cosθ

25=34+30cosθ

cosθ=0.3

Now,
(2A1+3A2)(3A12A2)=2A13A12A12A2+3A13A23A22A2

As, A1A2=A1A2cosθ

(2A1+3A2)(3A12A2)

=6A214A1A2cosθ+9A1A2cosθ6A22

=6A216A22+5A1A2cosθ

=6×326×52+5×3×5(0.3)

=118.5

Hence, (D) is the correct answer.

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