1. ## Calc(Vectors and stuff)

Here are some problems from a practice test that I couldn't get(Kept getting weird numbers), if anyone knows help would be appreciated

1. Find a vector V tangent to graph $\displaystyle f(x)=x^2+4x+3$ at the point (2, 19)

2. Object A is at $\displaystyle r(t)=<t^2+3t, 7-2t, 4cos(t-2)>$
Object B is at $\displaystyle s(t)=<5t, t^3-5, 3t-2>$
They crash at point (10, 3, 4) when t=2. What is the angle of the crash?

3. Determine the distance from P=(9, 2, 7) to the plane x+2y+3z=6

2. 1) Can you find a tangent vector? Think about the slope.
Can you then find a perpindicular direction? (m -> -1/m).

2) You know the dot-product, probably in two forms.
One algebraically and one more geometrical, with cos(a) in there.
Use both to set-up a formula for the angle between two vectors.

3) If you've seen it, use a known formula for the point-plane distance.
If not, find the equation of the line through the point perpindicular to the plane.
This will intersect the plane, you don't have to find a point-point distance.