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The vector vec c , directed along the ...

The vector ` vec c `, directed along the internal bisector of the angle between the vectors `vec a = 7 hati - 4 hatj - 4hatk and vecb = -2hati - hatj + 2 hatk " with " |vec c| = 5 sqrt(6),` is

A

`(5)/(3)(hati-hatj+hatk)`

B

`(5)/(3)(hati-7hatj+2hatk)`

C

`(5)/(3)(5hati+5hatj+2hatk)`

D

`(5)/(3)(-5hati+5hatj+3hatk)`

Text Solution

Verified by Experts

The correct Answer is:
B
Here, `c=t(hata+hatb)=t((7hati-4hatj-4hatk)/(9)+((-2hati-hatj+2hatk))/(3))`
`implies c =t((hati-7hatj+2hatk)/(9))`
also, `|c|=5sqrt(6)implies (t)/(9)*sqrt(1+49+4)=5sqrt(6)`
`therefore t=15 implies c=(15)/(9)(hati-7hatj+2hatk)`
or `=(5)/(3)(hati-7hatj+2hatk)`.
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