Q.

Let the plane ax+by+cz+d=0 bisect the line joining the points (4,-3,1) and (2,3,-5) at the right angles. If a,b,c,d are integers, then the minimum value of a2+b2+c2+d2 is

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answer is 28.

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Detailed Solution

ax+by+cz+d=0 Dr's :(-2,6,-6)=(1,-3,3) mid pt(3,0,-2) Equation of plane is 1(x-3)-3(y-0)+3(z+2)=0x-3-3y+3z+6=0x-3y+3z+3=0a=1,b=-3,c=3,d=3a2+b2+c2+d2=1+9+9+9=28
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