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.

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- May 6th 2011, 02:29 PMIanCarneyVectors question/confusion
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. - May 6th 2011, 02:37 PMVincentP
Try using this:

If 3 vectors lie on the same plane their Triple product is 0. - May 6th 2011, 02:42 PMmtpastille
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 :) - May 6th 2011, 02:55 PMPlato
- May 6th 2011, 07:41 PMSoroban
Hello, IanCarney!

Here is an elementary solution . . .

Quote:

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:

. . . . . .

. . .

. . . . . . . . . . .

Therefore: .