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Question

If A=(1,3,-5) and B=(3,5,-3), then the vector equation of the plane passing through the midpoint of AB and perpendicular to AB is

A
r.(^i+^j+^k)=2
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B
r.(^i+^j^k)=2
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C
r.(^i^j+^k)=2
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D
None
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Solution

The correct option is A r.(^i+^j+^k)=2
AB=OBOA=(3^i+5^j3^k)(^i+3^j5^k)=2^i+2^j+2^k
Midpoint of AB is (2, 4, -4)
Vector equation of the plane is [r(2^i+4^j4^k)].(2^i+2^j+2^k)=0
r.(^i+^j+^k)=2+44r.(^i+^j+^k)=2

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