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The plane denoted by ₁: 4 x+7 y+4 z+81=0 is rotated through a right angle about its line of intersection with the plane ₂: 5 x+3 y+10 z=25 . If the plane in its new position be denoted as , and the distance of this plane from origin is k , where k N , then ( k -12) / 100 is

Correct answer

2

Step-by-step solution

aligned & 4 x+7 y+4 z+81=0....(1) & 5 x+3 y+10 z=25.....(2) aligned Equation of plane passing through intersection of (1) and (2) aligned & (4 x+7 y++z+81)+ (5 x+3 y+10 z-25)=0 & (4+5 ) k+(7+3 ) y+(4+10 ) z+81-25 =0 aligned Plane (3) perpendicular to (1) aligned & So. 4(4+5 )+7(7+3 )+4(4+10 )=0 & =-1 & Putting =-1 in (3) & -x+4 y-6 z+106=0....(4) aligned distance of (4) from (0,0,0) aligned & k = 106 1+16+36 & k=212 aligned

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