
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 $\displaystyle r(t)=<t^2+3t, 72t, 4cos(t2)>$
Object B is at $\displaystyle s(t)=<5t, t^35, 3t2>$
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

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 dotproduct, probably in two forms.
One algebraically and one more geometrical, with cos(a) in there.
Use both to setup a formula for the angle between two vectors.
3) If you've seen it, use a known formula for the pointplane 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 pointpoint distance.