Home
Class 12
MATHS
If hati-3hatj+5hatk bisects the angle be...

If `hati-3hatj+5hatk` bisects the angle between `hata and -hati+2hatj+2hatk`, where `hata` is a unit vector, then

A

`a=(1)/(105)(41hati+88hatj-40hatk)`

B

`a=(1)/(105)(41hati+88hatj+40hatk)`

C

`a=(1)/(105)(-41hati+88hatj-40hatk)`

D

`a=(1)/(105)(41hati-88hatj-40hatk)`

Text Solution

Verified by Experts

The correct Answer is:
D
We must have `lamda(hati-3hatj+5hatk)=a+(2hatk+2hatj-hati)/(3)`
therefore, `3a=3lamda(hati-3hatj+5hatk)-(2hatk+2hatj-hati)`
`=hati(3lamda+1)-hatj(2+9lamda)+hatk(15lamda-2)`
or `3|a|=sqrt((3lamda+1)^(2)+(2+9lamda)^(2)+(15lamda-2)^(2))`
or `9=(3lamda+1)^(2)+(2+9lamda)^(2)+(15lamda-2)^(2)`
or `315lamda^(2)-18lamda=0 implies lamda=0, (2)/(35)`.
if `lamda=0,a=hati-2hatj-2hatk` (not acceptable).
for `lamda=(2)/(35),a=(41)/(105)hati-(88)/(105)hatj-(40)/(105)hatk`
Promotional Banner

Similar Questions

Explore conceptually related problems

The angle between the vector hati - hatj and hatj - hatk is :

If a=3hati-2hatj+hatk,b=2hati-4hatj-3hatk and c=-hati+2hatj+2hatk , then a+b+c is

Find the angle between the vectors hati-2hatj+3hatkand3hati-2hatj+hatk

If 4hati+ 7hatj+ 8hatk, 2hati+ 3hatj+ 4hatk and 2hati+ 5hatj+7hatk are the position vectors of the vertices A, B and C, respectively, of triangle ABC, then the position vector of the point where the bisector of angle A meets BC is

Find the sine of the angle between the vectors hati+2hatj+2hatkand3hati+2hatj+6hatk .

Let veca = 2hati + hatj -hatk , vecb = hati + 2hatj - hatk , and vecc = hati + hatj - 2hatk , be three vectors . A vector in the plane of b and c whose projection an a is of magnitude sqrt(2//3) is

A unit vector hata makes an angle pi/4 with z-axis, if hata+hati+hatj is a unit vector then hata is equal to