'N=8' + t oo o 0 Let S be the plane defined by y-z = 3, and let T be the plane defined by x-y+6z = 0. Find the vector equation for the line where S and T intersect.

Find the new equation of the line y=x after applying the translation by the vector (2, -1)

Suppose that a plane contains the points (5, 0, 0) and (0, 3, 1) and the line with the vector equation r = t < 2.5, 1.5, 0.5 >. What is the equation of the line?   Please explain your steps and show work.

Let / denote the line in R² with equation y = 3x - 2. Let Q = (2, -1). (a) Write the line / in vector form (i.e. of the form p = po + td where Po is a point on the line and d is a direction vector). (b) Find the distance from Q to 1. (c) Find the point on I closest to Q.