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Calculus 3: 3D Space

Consider the planes x + y + z = 1 and x - 2y + 3z = 1

a. Find the angle between the two planes

b. Find symmetric equations for the line of intersection of the two planes

1. Find a vector and parametric equations for the line that passes through (4,2) and is parallel to v = <-1,5>. Then find 2 other points on that line.

2. Find parametric equations for the line segment joining points P(2, -4, -1) and Q(5, 0, 7). Where does this line intersect the xy-plane?

Plot the point B(2,4,3)B(-2,-4,-3) in the 3D coordinate system.

Find the line through the points (5, -2, 3) and (7, 4, 1)

Plot the point P(2,4,3)P(2, 4, 3) in the 3D coordinate system.