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Lines whose equation are (x-3)/2=(y-2)/3...

Lines whose equation are `(x-3)/2=(y-2)/3=(z-1)/(lamda)` and `(x-2)/3=(y-3)/2=(z-2)/3` lie in same plane, then.
The value of `sin^(-1)sinlamda` is equal to

A

3

B

`pi-3`

C

4

D

`pi-4`

Text Solution

Verified by Experts

The correct Answer is:
D
Given lines are `(x-3)/(2)=(y-2)/(3)=(z-1)/(lambda).....(i)`
`and (x-2)/(3)=(y-3)/(2)=(z-2)/(3)......(ii)`
These lines lie in the same plane. So, both lines are coplanar.
`therefore |{:(,3-2,2-3,1-2),(,2,3,lambda),(,3,2,3):}|=0`
`Rightarrow |{:(,1,-1,-1),(,2,3,lambda),(,3,2,3):}|=0`
`Rightarrow 2(-3+2)-3(3+3)+lambda(2-3)=0`
`Rightarrow -2-18+5lambda=0 Rightarrow 5lambda=20`
`Rightarrow lambda=4`
`therefore sin^(-1) sin lambda=sin^(-1)sin4=sin^(-1) sin(pi-4)=pi-4`
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