Analytical Geometry – line equation parallel to two-plain intersection – Exercise 4428

Exercise

Consider the line equation passing through the point

$$(0,1,-1)$$

And parallel to the intersection of the plains

$$3x+y-2z=2$$

$$2x-y+3z+7=0$$

$$\frac{x-0}{1}=\frac{y-1}{-13}=\frac{z+1}{-5}$$