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Question

If a=^i+^j^k,b=^i+2^j+2^k & c=^i+2^j^k, find a unit vectors normal to the vectors a+b and b+c.

A
^i2^j+6^k40
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B
^i2^j+6^k41
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C
^i2^j+6^k41
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D
^i+2^j+6^k41
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Solution

The correct option is B ^i2^j+6^k41
a+b=3^j+^k
b+c=2^i+4^j+^k
Since we need a unit vector perpendicular to the vectors (3^j+^k) and (2^i+4^j+^k), we take their cross products.
(3^j+^k)×(2^i+4^j+^k)=6^k+3^i2^j4^i
=^i2^j+6^k
Unit vector thus becomes ^i2^j+6^k41

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