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Offline Centres

Q.

In R3,let L be a straight line passing through the origin. Suppose that all the points on L are at a constant distance from the two planes P1:x+2y−z+1=0 and .P2:2x−y+z−1=0 Let M be the locus of the feet of the perpendiculars drawn from the points on L to the plane P1 . Which of the following points lie(s) on M?

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a

0,−56,−23

b

−16,−13,16

c

−56,0,16

d

−13,0,23

answer is A.

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Detailed Solution

Let v¯ be the vector along L Then v→=i^j^k^12−12−11=i^−3j^−5k^ So any point on line L is Aλ,−3λ,−5λFoot of perpendicular from A to P (h,k,l), is h−λ1=k+3λ2=l+5λ−1=−λ−6λ+5λ+11+4+1=−16 ⇒h=λ−16,k=−3λ−13,l=−5λ+16 so foot is Pλ−16,−3λ−13,−5λ+16For λ=16,0, options1,2 satisfy P

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