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Let veca=hati-hatj,vecb=hati+hatj+hatk a...

Let `veca=hati-hatj,vecb=hati+hatj+hatk` and `vecc` be a vector such that `vecaxxvecc+vecb=vec0` and `veca.vecc=4`, then `|vecc|^(2)` is equal to:

A

9

B

8

C

`17/2`

D

`19/2`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `theta` be the anlge beween `veca` and `vecc`
`implies|vecb|^(2)=|vecc|^(2)|veca|^(2)sin^(2) theta` and `|vecc|^(2)|veca|^(2)cos^(2) theta=16`
`implies|veca|^(2)|vecc|^(2)=16+|vecb|^(2)implies|vecc|=19/2`
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