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Q.

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.
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