Given the following vector equation Without constructing its

Given the following vector equation:

Without constructing its general equation, show that this plane is equal to

Solution

Let us try to rewrite the given vector equation as the plane equation given

(x,y,z)

=(5,-7,0)+(1,1,-1)-(1,1,-1)+s(2,-2,3)-s(2,-2,3)+s(-1,1,-4)+t(1,1,4)-t(1,1,4)+t(2,2,-3)

=(1,1,-1)+(4,-8,1)+s(2,-2,3)+s(-3,3,-7)+t(1,1,4)+t(1,1,7)

=(1,1,-1)+s(2,-2,3)+t(1,1,4)+(4,8,-1)+s(-3,3,-7)+t(1,1,7)