# Math Help - Find Unit Vector and Angel

1. ## Find Unit Vector and Angel

Suppose that you are climbing a hill whose shape is given by , and that you are at the point (90, 50, 300).

In which direction (unit vector) should you proceed initially in order to reach the top of the hill fastest?
,
If you climb in that direction, at what angle above the horizontal will you be climbing initially (radian measure)?
__________.

help me understand and solve this one.

2. Originally Posted by DMDil
Suppose that you are climbing a hill whose shape is given by , and that you are at the point (90, 50, 300).

In which direction (unit vector) should you proceed initially in order to reach the top of the hill fastest?
,
If you climb in that direction, at what angle above the horizontal will you be climbing initially (radian measure)?
__________.

help me understand and solve this one.
The surface can be though of $F(x,y,z)=0.04x^2+0.02y^2+z-674$

The gradient will give the the direction of fastest increase

$\frac{\nabla F(90,50,300)}{|\nabla F(90,50,300)|}$