Consider the planes x_1 + x_2 + 3x_3 =4 and x_1 + 2x_2 + 4x_3 = 5 in r3 find parametric equations for the line of intersection of these two planes

You can solve for x and y in terms of z, then let z take on the value of the parameter.

Subtracting the first equation from the second, you get

... x_2 +x_3 = 1

Subtracting that from the first equation gives you

... x_1 +2x_3 = 3

Let x_3 = t. Then your parametric equations are ...

alright so i think for this one it would to draw it out. this may be hard for me to try and draw, but i will do my best on here:

        r

  /       |     \

notice how it forms 2 triangles inside one bigger triangle.

so if we know the angle spr is the same as psr that is saying the measure of angle p is the same as angle s. this means the big triangle psr is either isosceles or equilateral. in both cases, the triangle is perfectly symmetrical when split down the middle, which is in this case rq. because we know it is perfectly symmetrical on both sides, we know that the two triangles inside the bigger one are equal.