Find the magnitude of projection of vector 2i+3j+k, on a vector which is perpendicular to the plane containing vectors i+j+k and i+2j+3k.
A
√3√2
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B
√2√3
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C
4√3
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D
2√2√3
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Solution
The correct option is A√3√2 Normal vector to the plane to plane containing ^i+^j+^k and ^i+2^j+3^k is ¯n=(^i+^j+^k)×(^i+2^j+3^k) ¯n=^i−2^j+^k projection of (2^i+3^j+^k) on ¯n =∣∣
∣∣(2^i+3^j+^k).(^i−2^j+^k)√1+4+1∣∣
∣∣ =3√6=√32