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Consider a plane x+y-z=1 and point A(1, ...

Consider a plane `x+y-z=1` and point `A(1, 2, -3)`. A line L has the equation `x=1 + 3r, y =2 -r and z=3+4r`. the equation of plane containing line Land point A has the equation x − 3 y + 5 = 0 x + 3 y − 7 = 0 3 x − y − 1 = 0 3 x + y − 5 = 0

A

`x-3y+5=0`

B

`x+3y-7=0`

C

`3x-y-1=0`

D

`3x+y-5=0`

Text Solution

Verified by Experts

The correct Answer is:
b
The equation of plane containing the line L is
`" "A(x-1)+ B(y-2) + C(z-3)=0`,
where `3A-B+4C=0" "` (i)
(i) also contains point `A(1, 2, -3)`.
Hence, C =0 and `3A= B`.
The equation of plane is `x-1+ 3(y-2) =0 or x+ 3y-7=0`
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