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Find the point where the line (x-1)/2=(y...

Find the point where the line `(x-1)/2=(y-2)/-3=(z+3)/4` meets the plane `2x+4y-z=1`.

A

`(3,-1,1)`

B

`(3,1,1)`

C

`(1,1,3)`

D

`(1,3,1)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let the intersection point of plane and line (a,b,c), then
`2a+4b-c=1` . .. (i)
Give equation of line is `(x-1)/(2)=(y-2)/(-3)=(z+3)/(4)=k" "` [say]
Also, point of intersections (a,b,c) satisfy the equation of line
then, `a=2k+1,b=-3k+2`
`and" "c=4k-3" "` (where, k is constant)
On substituting these values in Eq. (i), we get
`2(2k+1)+4(-3k+2)(4k-3)=1rArrk=1`
Hence, required point is (3,-1,1).
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