Question

Find parametric equations for the line of intersection of the planes 2x-y+3z=5 and 3x-2y-z=7

Answer 1

The equation of line is

x= 3-7t,y=1-11t and z-t

Step-by-step explanation:

The equations of two planes are

2x-y+3z= 5

3x-2y-z=7

Setting z= t

∴ 2x-y+3t=5               and          3x-2y -t= 7

⇒2x-y=5- 3t...........(1)               ⇒3x-2y = 7+t.............(2)

Equation (1) ×2 - Equation(2)

4x-2y -(3x-2y) = 10-6t-(7+t)

⇒4x-2y-3x+2y=10 - 6t - 7-t

⇒x= 3-7t

putting the value of x in equation (1)

2(3-7t)-y+3t=5

⇒6-14t + 3t-5=y

⇒y=1-11t

The equation of line is

x= 3-7t,y=1-11t and z-t