Vectors-intersection of two planes

[ishterz]

Vectors-planes and lines

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1. Homework Statement

Two planes have equations
2x-y-3z=7
x+2y+2z=0

Find a vector equation for their line of intersection

3. The Attempt at a Solution

I haven't learned the vector product in class but read it and attempted it and got the direction vector 4i-7j+5k.
However, I don't know how to get the position vector of this.



Thank you for your help and time

 

[Sethric]

See my response in your other thread.

 

[HallsofIvy]

Actually, I would think it would be easier to get the "position vector", xi+ yj+ zk, than the direction vector. Your two equations are 2x-y-3z=7 and
x+2y+2z=0. Those are two equations in three unknowns. You can solve for two of the unknowns in term so the third which is exactly what you need for a one dimensional line. Multiply the first equation by two and add the second:
(4x- 2y- 6z)+ (x+ 2y+ 2z)= 5x- 4z= 14+ 0= 14.

We have eliminated y. Now, solve that equation for z: 4z= 5x- 14 so z= (5/4)x- 7/2.

Put that back into 3x- y- 3z= 7: 3x- y- (15/4)x+ 21/4= 7.

Solve for y and write the position vector xi+ yj+ zk using x as parameter.