Consider the three planes P1:3x+15y+21z=9 P2:x−3y−z=5 P3:2x+10y+14z=5 Then , which one of the following is true ?
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a
P1 and P2 are parallel
b
P1 and P3 are parallel
c
P2 and P3 are parallel
d
P1,P2 and P3 all are parallel
answer is B.
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Detailed Solution
The direction ratios of normal to the planeax+by+cz+d=0 are a,b,cThe direction ratios of normal to the planeP1:3x+15y+21z=9 are 1,5,7The direction ratios of normal to the planeP2:x−3y−z=5 are 1,−3,−1The direction ratios of normal to the planeP3:2x+10y+14z=5 are 1,5,7Observing the above three planes, direction ratios of normal lines of the planes P1 and P3 are proportional. Hence, the planes P1,P3 are parallel.