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Question

V=2^i+^j^k and W=^i+3^k. If U is a unit vector, then the maximum value of the scalar triple product [U V W] is


A

-1

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B

10+6

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C

59

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D

60

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Solution

The correct option is C

59


Given V=2^i+^j^k and W=^i+3^k
[U V W]=U.[(2^i+^j^k)×(^i+3^k)]U.(3^i7^j^k)=|U||3^i7^j^k| cos θ
which is maximum, if angle between U and 3^i7^j^k is 0 and maximum value
=|3^i7^j^k|=59


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