Hello I need help with the following:
u = 2i +3j v= -i + 2j
Find a cartesian equation for the plane P containing the point Q(1,2,3) and parallel to u and w.
Find the perpendicular distance between the plane P and the origin
Do you know what a cross product is?
You could use it to get a vector that is orthogonal to both u and w.
However in this case, itīs clear that both u and v are in the xy plane so to speak. So you will get a normal pointing "straight up" from the xy-plane.
You will need your normal to satisfy . So you get . Note here that the means dot-product.
So you have a plane parallell to the xy-plane, with perpendicular distance of 3 to the origin.
Are you sure of the wording of this problem?
As given, it is too simple . . .
(a) Find a cartesian equation for the plane containing the point
. . . and parallel to and
Since and are in the -plane, then plane is parallel to the -plane.
Since plane contains , its equation is: .
(b) Find the perpendicular distance between the plane and the origin
The point on plane nearest the origin is
Its distance from the origin is