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Question

The unit vector which, is perpendicular to the vectors A=^i2^j+^k and B=3^i2^j^k is

A
13(^i^j+^k)
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B
13(^i+^j+^k)
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C
13(^i+^j^k)
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D
13(^i^j^k)
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Solution

The correct option is B 13(^i+^j+^k)
We know that the unit vector perpendicular to two vectors is given as
^n=A×B|A×B|
So, we have A×B as per determinant method as
^i^j^k121321
(2(2))^i(13)^j+(2(6))^k
4^i+4^j+4^k
Also, |A×B|=42+42+42=43
Hence, ^n=A×B|A×B|=4^i+4^j+4^k43=13(^i+^j+^k)

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