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The position vectorof the point where th...

The position vectorof the point where the line `vec(r)=hat(i)-hat(j)+hat(k)+t(hat(i)+hat(j)-hat(k))` meets the plane `vec(r)*(hat(i)+hat(j)+hat(k))=5`, is

A

`5hat(i)+hat(i)-hat(k)`

B

`5hat(i)+3hat(j)-3hat(k)`

C

`2hat(i)+hat(j)+2hat(k)`

D

`5hat(i)+hat(j)-hat(k)`

Text Solution

Verified by Experts

The correct Answer is:
B
Given `vec(r)=(hat(i)-hat(j)+hat(k))+t(hat(i)+hat(j)-hat(k))`
`=(1+t)hat(i)-(1-t)hat(j)+(1-t)hat(k)`
Also, `vec(r).(hat(i)+hat(j)+hat(k))=5`
Since line meets the plane therefore `vec(r)` satisfy the equation of plane.
`:.(1+t)-(1-t)+(1-t)=5`
`rArr" "1+t=5rArrt=4`
`:." "vec(r)=(1+4)hat(i)-(1-4)hat(i)+(1-4)hat(k)=5hat(i)+3hat(j)-3hat(k)`
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