Calculate the eq'n of the intersection line between 2 planes which are not parallel?

Question

If
Pi1: 3x-2y+z-5=0
Pi2: x+y - 2z +3=0

If the two planes are not parallel, what is the equation of the intersection line?

Sorry I posted this in the wrong section ><

Answer 1

3x-2y+z-5=x+y-2z+3
2x-3y+3z=8

Answer 2

Find the equation of the line of intersection of the two planes.

3x - 2y + z - 5 = 0
x + y - 2z + 3 = 0

The directional vector v, of the line will be normal to the normal vectors n1 and n2, of both planes. Take the cross product.

v = n1 X n2 = <3, -2, 1> X <1, 1, -2> = <3, 7, 5>

Now find a point on the line. It will be a point the two planes have in common. Let y = 0 and solve for x and z.

Add twice the first equation to the second.

3x + z - 5 = 0
x - 2z + 3 = 0

The solution for this set is:
(x, y, z) = P(1, 0, 2)

With the directional vector v, of the line and a point P on the line we can write its equation.

L(t) = P + tv
L(t) = <1, 0, 2> + t<3, 7, 5>
where t is a scalar ranging over the real numbers

Answer 3

hit upon the equation of the line of intersection of the two planes. 3x - 2y + z - 5 = 0 x + y - 2z + 3 = 0 The directional vector v, of the line could be regularly occurring to the wide-unfold vectors n1 and n2, of the two planes. Take the bypass product. v = n1 X n2 = <3, -2, a million> X = <3, 7, 5> Now hit upon a element on the line. it is going to likely be a element the two planes have in uncomplicated. enable y = 0 and decide for x and z. upload 2 cases the 1st equation to the 2d. 3x + z - 5 = 0 x - 2z + 3 = 0 the respond for this set is: (x, y, z) = P(a million, 0, 2) With the directional vector v, of the line and a element P on the line we can write its equation. L(t) = P + television L(t) = + t<3, 7, 5> the placement t is a scalar ranging over the genuine numbers