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Let P=0 be the equation of a plane passi...

Let `P=0` be the equation of a plane passing through the line of intersection of the planes `2x-y=0a n d3z-y=0` and perpendicular to the plane `4x+5y-3z=8.` Then the points which lie on the plane `P=0` is/are a. `(0,9,17)` b. `(1//7,21//9)` c. `(1,3,-4)` d. `(1//2,1,1//3)`

Text Solution

Verified by Experts

The equation of the plane through the line of intersection of the planes `2x - y = 0 and 3z - y = 0 `
may be written as `(2x-y) +k(3z - y) = 0`
`rArr 2x -(1+k)y+3kz =0`
which will be perpendicular to the plane
`4x + 5y- 3z 8`
if `8 - 5(1+k) - 9k = 0`
`rArr 8 - 5 -5k - 9k =0`
`rArr k= 3/14`
Raquired equation of the plane is
`2x-(1+3/14)y+3 (3)/14 z=0`
`rArr 28 x - 17 y +9z = 0.`
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