Find an equation of the straight line through(1,-3,5)

Question

and parallel to both planes x-2y+z=2 and 2x+y-3z=5?

Answer 1

Step 1:

The line passes through the point .

The plane equations are

.

.

The cross product of two normal vectors is the direction vector for the line of intersection.

The normal vectors of two planes are

.

.

The cross product of two vectors is

The directional vector of two planes is .

Step 2:

The line equation passes through point  and direction vector is

.

The line equation passes through point and directional vector is

.

The line equation is .

Solution:

The line equation is .