Find the vector equation for the line of intersection of the planes 4x+3y−3z=−5 and 4x+z=5
r = < _, _, 0> + t<3, _, _>
Fill in the blanks for the vector equation.
The Attempt at a Solution
I used the method of elimination of linear systems.
4x + 3y - 3z = -5 (1)
4x +0y +z = 5 (2)
Subtract equation (1) from equation (2)
(1) - (2)
3y - 4z = -10
y = 4z/3 -10/3
Next I isolate x from equation (2)
x = -z/4 + 5/4
Let z = t as parameter
x(t) = -t/4 + 5/4
y(t) = 4z/3 - 10/3
z(t) = t
From this I know that the point on the line of intersection is (5/4, -10/3, 0)
However for the vector of the line of intersection, I keep on getting the x value as -1/4 and the answer is 3.