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Question

|a|=|b|=5 and the angle between a and b is π4. The area of the triangle constructed on the vectors a-2b and 3a+2b is?


A

50

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B

502

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C

502

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D

100

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Solution

The correct option is B

502


Finding the area of the triangle:

Given, |a|=|b|=5 and angle between a&bis π4. Also the sides a-2b and 3a+2b.

By using formula for area of triangle is 12×|AB×BC|

=12×a-2b×3a+2b=12×3a×a+2a×b-6b×a-4b×b=12×2×0+2a×b-6b×a-4×0(a×a=0=b×b)=12×2a×b+6a×b(a×b=-b×a)=12×8a×b=4absinθ(a×b=absinθ)=4×5×5×sinπ4=4×5×5×12=1002×22=502

Therefore, correct answer is option (B).


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