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Question

The unit vector which is perpendicular to the vectors A=^i+2^j^k and B=3^i2^j+^k is

A
15(^j2^k)
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B
(^j2^k)
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C
15(^j+4^k)
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D
(^j+4^k)
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Solution

The correct option is A 15(^j2^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
(22)^i(1(3))^j+(26)^k
4^j8^k
Also, |A×B|=(4)2+(8)2=80=45
Hence, ^n=A×B|A×B|=4^j8^k45=15(^j2^k)

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