Linear Algebra

[milosmathss]

can anyone help me with either of these questions, I am very stuck?
Let L be the line of intersection between the planes
2x−3y−2z=1,
4x+2y+2z=6.

(a) Find a vector 'v' parallel to L.

(b) Find the cartesian equation of a plane through the point (3,−1,2)(3,−1,2) and perpendicular to L

 

[Dr.Peterson]

can anyone help me with either of these questions, I am very stuck?
Let L be the line of intersection between the planes
2x−3y−2z=1,
4x+2y+2z=6.

(a) Find a vector 'v' parallel to L.

(b) Find the cartesian equation of a plane through the point (3,−1,2) and perpendicular to L

What are the normal vectors to those planes?

How is vector v related to those vectors?

What is the equation of a plane perpendicular to a given vector?

Please show some work, so we can see what help you need:

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[HallsofIvy]

You are given that 2x- 3y- 2z= 1 and 4x+ 2y+ 2z= 6.
Adding the two equations, 6x- y= 7 so y= 6x- 7. Replacing y by 6x- 7 in the first equation, 2x- 3(6x- 7)- 2z= -16x+ 21- 2z= 1. 2z= -16x+ 20 so z= -8x+ 10.

Parametric equations for the line of intersection of the two planes are
x= t, y= 6t- 7, and z= -8t+ 10.

Can you finish the problem?