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Consider a plane P:2x+y-z=5, a line L:(x...

Consider a plane `P:2x+y-z=5`, a line `L:(x-3)/(2)=(y+1)/(-3)=(z-2)/(-1)` and a point `A(3, -4,1)`. If the line L intersects plane P at B and the xy plane at C, then the area (in sq. units) of `DeltaABC` is

A

0

B

`14/3`

C

`3/7`

D

`7/3`

Text Solution

Verified by Experts

The correct Answer is:
D
Equation of line `L_(2)` is `(x-3)/1=(y+4)/(-3)=(z-1)/(-1)`
(1) Equation of plane containing `L_(1)` & `L_(2)`
`|(x-3, y+1, z-2),(0,3,1),(-1,6,2)|=0implies+3z-5=0`
(2) Volume of tetrahedron `=1/6 |(3,-4,1),(5,-4,1),(7,-7,0)|=7/3`
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