Determine the value for such that the point A(-1,3,4), B(-2,3,-1), and C(-5,6, ) all lie on a plane that contains the origin.
I'm not sure what they're asking for. The answer in the book is -7.
You have four points: A, B, C and O (origin). The question is asking for a plane, so try to find an equation of a plane that involves all of these four points. Start by constructing two vectors from these points, say and . Then find a Cartesian equation of this plane (i.e., in the form ). Since the plane intersects the origin, D=0. See if you can then solve the equation for x.
Edit: I suppose VincentP's method is more sophisticated, but both work
Here is an elementary solution . . .
Determine the value for such that the points
all lie on a plane that contains the origin. . (Answer: -7)
A plane has the general equation: .
. . If the plane contains the Origin, then
. . . .
The equation of the plane through with is:
. . . . . .
. . .
. . . . . . . . . . .