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Question

Find the vector and Cartesian equations of the plane passing through the points with position vectors
3i+4j+2k,2i2jk, and 7i+j+k

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Solution

Equation f the perpendicular to the plane

n=∣ ∣ ∣ijk163431∣ ∣ ∣=3i13j+27k

Equation of plane passing through three given points is given by:

(n)(rro)=0

(3i13j+27k)((x3)i+(y4)j+(z2)k)=0

Cartesian form of plane :

=3(x3)13(y4)+27(z2)=0=3x13y+27z+7=0

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