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Question

If the points (αx,α,α) , (α,αy,α) , (α,α,αz) and (α1,α1,α1) are coplanar αR then

A
xy+yz+zx=1
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B
1x+1y+1z=1
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C
11x+11y+11z=1
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D
xyz=1
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Solution

The correct option is D 1x+1y+1z=1
V=(x,y,0)
U=(0,y,z)
W=(1,1,z1)
0=∣ ∣xy00yz11z1∣ ∣ (for coplanar property)
=x(y(z1)z)+y(z)
=x(yzyz)+(zy)
0=xyzyxxzzy
1=1x+1y+1z

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