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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-7hatj+2hatk)`

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
Let `a=7hati-4hatj-4hatk`
and `b=-2hati-hatj+2hatk`
Now, required vector `c=lamda((a)/(|a|)+(b)/(|b|))`
`=lamda((7hati-4hatj-4hatk)/(9)+(-2hati-hatj+2hatk)/(3))`
`=(lamda)/(9)(hati-7hatj+2hatk)`
`|c|^(2)=(lamda^(2))/(81)xx54=150`
`implies lamda=+-15`
`impliesc=+-(5)/(3)(hati-7hatj+2hatk)`.
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