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Question

If a=^i+2^j3^k and b=3^i^j+2^k then the angle between the vectors a+b and ab is.

A
60o
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B
90o
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C
45o
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D
55o
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Solution

The correct option is B 90o
Given that:
a=^i+2^j3^k and b=3^i^j+2^k
Now,
a+b=^i+2^j3^k+3^i^j+2^k=4^i+^j^k
ab=^i+2^j3^k3^i+^j2^k=2^i+3^j5^k
Then,
(a+b).(ab)=(4^i+^j^k).(2^i+3^j5^k)
=8+3+5
=0
So, angle between a+b and ab is 90.
Hence, B is the correct option.

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