Hello, Jenny!
Find an equation for the plane passing through the point P(0,4,1)
which is parallel to the vectors u = <1,2,3> and v = <0,-1,1>.
Since the plane is parallel to u and v,
. . its normal vector n is perpendicular to both u and v.
Then n is the cross product of u and v.Code:| i j k | n = | 1 2 3 | = 5i - j - k = <5,-1,-1> | 0 -1 1 |
You have a point P(0,4,1) and normal vector n = <5,-1,-1>
You can write the equation: .5(x - 0) - 1(y - 4) - 1(z - 1) .= .0