Calculus 3

The position of a particle in the xy plane at time t is $\vec{r}(t) = (t+1)\mathbf{i} \, + \, (t^2-1)\mathbf{j}$ Find an equation in x and y whose graph is the path of the particle. Then find the particle's velocity and acceleration vectors at t = 1.

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

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

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