Find the vector equation of the plane through the points (2, 1, -1) and (-1, 3, 4) and perpendicular to the plane `x-y+4z=10.`

Explanation

Let us assume the equation of plane through (2,1,-1) be a(x-2)+b(y-1)+c(z+1)=0..(i)

Since, (i) passes through (-1,3,4)

`a(-1-2)+b(3-1)+c(4+1)=0`

`Rightarrow-3 a+2 b+5 c=0...(ii)`

Also, since plane (i) is perpendicular to plane x-2 y+4 z=10 a-2 b+4 c=0...(iii)

From (ii) and (iii) we have,


` frac{a}{8+10}+frac{b}{5+12}=frac{c}{6-2} `

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