Question
Find an equation for the plane passing through the point (0,4,1) which is parallel to the vectors <1,2,3> and <0,-1,1>.
Could you please teach me do this question? Thank you very much.
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