InterviewSolution
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InterviewSolution
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In `R^(3)`, consider the planes `P_(1):y=0` and `P_(2),x+z=1.` Let `P_(3)` be a plane, different from `P_(1)` and `P_(2)` which passes through the intersection of `P_(1)` and `P_(2)`, If the distance of the point (0,1,0) from `P_(3)` is 1 and the distance of a point `(alpha,beta,gamma)` from `P_(3)` is 2, then which of the following relation(s) is/are true?A. `2alpha+beta+2gamma+2=0`B. `2alpha+beta+2gamma+4=0`C. `2alpha+beta+2gamma-10=0`D. `2alpha+beta+2gamma-8=0` |
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Answer» Correct Answer - B::D b.,d Clearly , planr `P_(3) is P_(2) + lamdaP_(1) =0` . `implies x+ lamday+z-1=0` Distance of this from point `(0,1,0)`is 1, `=(0+lamda+0-1)/(sqrt(1+lamda^(2)+1))=+_1` `therefore lamda =-(1)/(2)` thus , equation of `P_(3)is 2x-y+2z-2=0` DIstance of this plane from point `(alpha, beta,gamma)`is 2. `=|(2alpha-beta+2gamma-2)/(3)|=2` `implies 2alpha-beta+2gamma=2+-6` thus options (b) and (d) are correct. |
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