InterviewSolution
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InterviewSolution
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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 `P_1 : x + 2y-z +1 = 0` and `P_2 : 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 `P_1`. Which of the following points lie(s) on M?A. `(0,-(5)/(6),-(2)/(3))`B. `(-(1)/(6),-(1)/(3),(1)/(6))`C. `(-(5)/(6),0,(1)/(6))`D. `(-(1)/(3),0,(2)/(3))` |
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Answer» Correct Answer - A::B a.b . Let `vecv` be the vetor along I. `P_(1):x+2y-Z+1=0 and P_(2):2x-y+z-1=0` ` therefore vecc=|{:(hati,hatj,hatk),( 1,2,-1),( 2,-1,1)}|= hati-3hatj-5hatk` since I. is through origin any point on line I. is `A(lamda,3lamda ,-5lamda).`Foot of perpendicular from A to `P_(1)` , is `(h- lamda)/( 1)`=(k+3lamda)/(-1)=-(lamda-6lamda+5lamda+1))/(1+4+1)=-(1)/(6)` `therefore h= lammda-(1)/(6) ,k =- 3lamda -(1)/(3) ,il=-5 lamda+(1)/(6)` so, foot ro rpoint on lovus M is `(lamda-(1)/(6),-3lamda-(1)/(3)-(1)/(3),-5lamda+(1)/(6))` So points (a) and (b) lie on this loucs . |
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