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let P be the plane, which contains the l...

let P be the plane, which contains the line of intersection of the planes `x+y+z-6=0` and `2x+3y+z+5=0` and it is perpendicular to the xy-plane thent he distance of the point (0,0,256) from P is equal to

A

`(17)/(sqrt(5))`

B

`63 sqrt(5)`

C

`(11)/(sqrt(5))`

D

`205 sqrt(5)`

Text Solution

Verified by Experts

The correct Answer is:
C
Equation of required plane is `P_(1) + lambda P_(2) = 0`
`2x + 3y + z 5 + lambda (x + y + z - 6) = 0`
`vec(lambda) = (2 + lambda) hat(i) + (3 + lambda) hat(j) + (1 + lambda) hat(k)`
`vec(lambda).hat(k) = 0, lambda = - 1`
Equation of plane `= x + 2y + 11 = 0`
Distance `= (11)/(sqrt(1^(2) + 2^(2))) = (11)/(sqrt(5))`
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