Family of Planes Passing through the Intersection of Two Planes
The vector eq...
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^i−9^j+^k)=1 and ¯r.(^i+4^j−2^k)=2 is:
A
¯r.(2^i+7^j−13^k)=1
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B
¯r.(2^i−7^j−13^k)=1
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C
¯r.(2^i−7^j+13^k)=0
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D
¯r.(7^i−9^j+13^k)=0
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Solution
The correct option is B¯r.(2^i−7^j−13^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^j−2^k)=2 ∴¯n=(3^i−^j+^k)×^i+4^j−2^k≡−2^i+7^j+13^k ∴ Required plane is ¯r.(2^i−7^j−13^k)=1