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If vecV=2vec i+ vec(j) - vec(k) " and "...

If ` vecV=2vec i+ vec(j) - vec(k) " and " vec(W) = vec(i) + 3vec(k)` . if` vec (U)` is a unit vectors then the maximum value of the scalar triple product `[vec(U) , vec(V) , vec(W)]` is

A

`(-1)/(sqrt(59))`

B

`sqrt(10) + sqrt(6)`

C

`sqrt(59)`

D

`sqrt(60)`

Text Solution

Verified by Experts

The correct Answer is:
C
Given `vec( V) = 2hat(i) + hat(j) - hat(k) " and " vec(W) = hat(i) + 3hat(k)`
`[vec(U)vec(V) vec(W)] = vec(U) . [(2hat(i) + hat(j) -hat(k)) xx (hat(i) + 3hat(k))]`
`=vec(U) .(3hat(i) -7hat(j) - hat(k)) = |vec(U)||3hat(i) - 7 hat(j) - hat(k)|` cos 0
Which is maximum if angle between `vec(U) " and " 3hat(i) - 7hat(j) - hat(k) `
is 0 and maximum value
`+|3hat(i) -7hat(j) - hat(k)|= sqrt(59)`
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