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Question

The magnitude of the projection of the vector 2^i+3^j+^k on the vector perpendicular to the plane containing the vectors ^i+^j+^k and ^i+2^j+3^k, is:

A
36
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B
32
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C
6
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D
32
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Solution

The correct option is D 32
The vector perpendicular to the given vector is
a=∣ ∣ ∣^i^j^k111123∣ ∣ ∣

a=^i2^j+^k
Projection of b on a=|ab||a|
=|(^i2^j+^k)(2^i+3^j+^k)|6
=|26+1|6
=32

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