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Question

The vector equation of the plane passing through the intersection of the planes r(^i+^j+^k)=1 and r(^i2^j)=2, and the point (1,0,2) is

A
r(^i7^j+3^k)=73
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B
r(^i+7^j+3^k)=7
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C
r(3^i+7^j+3^k)=7
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D
r(^i+7^j+3^k)=73
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Solution

The correct option is B r(^i+7^j+3^k)=7
Family of planes passing through intersection of the given planes is
{r(^i+^j+^k)1}+λ{r(^i2^j)+2}=0
The above curve passes through ^i+2^k.
(31)+λ(1+2)=0
λ=23
Hence, equation of the plane is
3{r(^i+^j+^k)1}2{r(^i2^j)+2}=0
r(^i+7^j+3^k)=7

TRICK: Only option r(^i+7^j+3^k)=7 satisfies the point (1,0,2)

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