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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

`+-3c`

B

`+-(3)/(2)c`

C

`+-c`

D

`+-(2)/(3)c`

Text Solution

Verified by Experts

The correct Answer is:
C
let `r=lamdac`
Given `|r|=|lamda||c|`
`therefore(|a+c|)/(2)=|lamda||c|`
`therefore|6hati-2hatj-4hatk|=2|lamda|3hati-hatj+2hatk|`
`therefore sqrt(56)=2|lamda|sqrt(14)`
`therefore lamda=+-1`
`therefore r=+-c`.
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