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Question

The vector equation of the plane through the point ^i+2^j^k and perpendicular to the line of intersection of the plane ¯r.(3^i9^j+^k)=1 and ¯r.(^i+4^j2^k)=2
is:

A
¯r.(2^i+7^j13^k)=1
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B
¯r.(2^i7^j13^k)=1
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C
¯r.(2^i7^j+13^k)=0
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D
¯r.(7^i9^j+13^k)=0
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Solution

The correct option is B ¯r.(2^i7^j13^k)=1
Equation of plane through the point (^i+2^j^k) is (¯r(^i+2^j^k)).¯n=0
Where ¯n is normal to the plane. Required plane is perpendicular to the line of intersection of the planes
¯r.(3^i^j+^k)=1 and ¯r.(^i+4^j2^k)=2
¯n=(3^i^j+^k)×^i+4^j2^k2^i+7^j+13^k
Required plane is ¯r.(2^i7^j13^k)=1

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