- #1

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## Homework Statement

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.

## Homework Equations

## 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

Isolate y:

**y = 4z/3 -10/3**

Next I isolate x from equation (2)

**x = -z/4 + 5/4**

Let z = t as parameter

Parametric equation:

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.