Given a position vector rt t t2 t3 find the velocity and

Question

1. Find the equation of the plane that contains the point P (2,4,6) and the line

x = 7 - 3t, y = 3 + 4t, z = 5 + 2t.

2. Find the equation of the line passing through the points P (3,5,7) and Q (6,5,4).

3. Given a position vector

r(t) = [t, t², t³]

Find the velocity and acceleration vectors and the speed at time t.

4. Find the shortest distance from the point (2,5,7) to the line

x(t) = 6 - 2t, y(t) = 4 + 5t, z(t) = 4 + t.