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Question

Find the Cartesian equation of the following planes:
r(^i+^j^k)=2.

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Solution

It is given that equation of the plane is
r.(^i+^j^k)=2.....(1)
For any arbitrary point P(x,y,z) on the plane, position vector r is given by,
r=x^i+y^jz^k
Substituting the value of r in equation (1), we obtain
(x^i+y^jz^k).(x^i+y^jz^k)=2
x+yz=2
This is the Cartesian equation of the plane.

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