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Let veca=(1,1,-1), vecb=(5,-3,-3) and ve...

Let `veca=(1,1,-1), vecb=(5,-3,-3)` and `vecc=(3,-1,2)`. If `vecr` is collinear with `vecc` and has length `(|veca+vecb|)/(2)`, then `vecr` equals

A

`+-3vecc`

B

`+-3/2vecc`

C

`+-vecc`

D

`+-2/3vecc`

Text Solution

Verified by Experts

The correct Answer is:
C
We have, `vecr=lambdavecc`
Given, `|vecr|=|lambda||vecr|`
`therefore |6hati-2hatj-hatk|=2|lambda||3hati-hatj+2hatk|`
`therefore sqrt(56) = 2|lambda|sqrt(14)`
`therefore lambda=+-1`
`therefore vecr=+-vecc`
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