(a) Find parametric equations for the line through (1, 4, 4) that is perpendicular to the plane x − y + 2z = 7. (Use the parameter t.)
(b) In what points does this line intersect the coordinate planes?

Step-by-step explanation:

A vector perpendicular to the plane ax+by+cz+d=0 is of the form .

So, a vector perpendicular to the plane x − y + 2z = 7 is .

The parametric equations of a line through the point and parallel to the vector are as follows:

Put and

Therefore,

xy-plane:

Put z = 0 ⇒ t = -2 ⇒x = - 1 , y = 6

So, at point (-1,6,0)

yz-plane:

Put x = 0 ⇒ t = -1 ⇒ y = 5, z =2

So, at point (0,5,2)

xz-plane:

Put y = 0 ⇒ t = 4 ⇒ x = 5, z = 12

So, at point (5,0,12)

tube or goog would be a great resource to with that question