Question

The three vectors u=3i-j+k, v=i+2j-k, w=i+j+k are drawn from the origin. What is the equation of the plane through their endpoints? 


The answer is 2x+2y+z=5. Could you explain how to get this answer? (Particularly where the 5 comes from)

 

Answer 1

Calculate uv vector,

uv=(i+2j-k)-(3i-j+k )=-2i+3j-2k

Calculate vw vector,

vw=(i+j+k )-(i+2j-k)=-j+2k

uvxvw=(-2i+3j-2k)x(-j+2k)

       =4i+4j+2k

Perpendicular unit vector,<4,4,2>

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Equation of the plane,

4(x-1)+4(y-1)+2(z-1)=0

4x-4+4y-4+2z-2=0

4x+4y+2z=10

Divide each aide by 2

2x+2y+z=5