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If A(-4,0,3)a n dB(14 ,2,-5), then which...

If `A(-4,0,3)a n dB(14 ,2,-5),` then which one of the following points lie on the bisector of the angle between ` vec O Aa n d vec O B(O` is the origin of reference )? a. `(2,2,4)` b. `(2, 11 ,5)` c. `(-3,-3,-6)` d. `(1,1,2)`

A

`(2, 2, 4)`

B

`(2, 11, 5)`

C

`(-3, -3, -6)`

D

`(1, 1, 2)`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
`vec(OA) = -4hati + 3hatk, vec(OB) = 14hati + 2hatj- 5hatk`
`hata = (-4hati+3hatk)/(5), hatb = (14hati + 2hatj- 5hatk)/(15)`
`vecr= (lamda )/(15) [-12hati+ 9hatj + 14hati + 2hatj -5hatk]`
`" " = (lamda)/(15) [2hati +2hatj+4hatk]`
`" "= (2lamda)/(15) [ hati +hatj +2hatk]`
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