Q.

Find the constant k so that the planes x–2y+kz=0 and 2x + 5y – z = 0 are at right angles.

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Detailed Solution

Given planes x - 2y + kz = 0 .... (1)

compare with a1x+b1y+c1z+d1=0
Where a1=1,b1=2,c1=k 2x+5yz=0 ...(2) compare with a2x+b2y+c2z+d2=0 Where a2=2,b2=5,c2=1
Planes (1) & (2) are perpendicular then cosθ=0
a1a2+b1b2+c1c2=01(2)+(2)5+k(1)=0210k=08k=0k=8

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