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Question

Find the equation of the plane through the intersection of the planes.
r(^i+3^j^k)=9 and r(2^i^j+^k)=3 and passing through the origin.

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Solution

Plane P1:r.(^i+3^j^k)=9
Cartesian equation of plane P1:x+3yz9=0
Plane P2:r.(2^i^j+^k)=3
Cartesian equation of plane P2:2xy+z3=0
Equation of plane passing through the intersection of two planes is:
P:P1+k(P2)=0x+3yz9+k(2xy+z3)=0.......(1)
P passes through origin
put (0,0,0) in the eq(1),
9+k(3)=0k=3
P:x+3yz9+(3)(2xy+z3)=05x+6y4z=05x6y+4z=0

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