Homework SourseFind the equation of the plane containing the point A103 and
Find the equation of the plane containing the point A(1,0,-3) and the line L given by the parametric equations
x=2+t,
y=-1-3t,
z=6+2t
x=2+t,
y=-1-3t,
z=6+2t
Solution
the line passes through B(2,1,6) and is parallel to v (1,-3,2) vector AB= (1,1,9) The normal to the plane is parallel to AB x v ( cross product) n =(i+j+9k) * (i-3j+2k) = -3k-2j + (-k+2i)+ 9j +27i = 29i +7j-4k let C(x,y,z) be on the plane then AC is perpendicular to n => {(x-1)i+ yj + (z+3) k} . (29i+7j-4k)=0 => 29(x-1) + 7y -4(z+3)=0 => 29x+7y-4z=41
