Thread: Beginner Vector Calculus things

This is just the start up of Vector. Where they show you vectors and what not in 3d, etc

This is very basic stuff but im stumped:

A plane is heading due east and climbing at the rate of 80 km/hr. Suppose its airspeed is 525 km/hr and there is a wind blowing 100 km/hr to the northeast.

(a) What is the velocity of the plane relative to the ground? Give your answer correct to 2 decimal places.

Answer should be in the form of ai + bj + ck. I got the b and c part. I can't figure out the a coefficient. c is obviously 80. b is 70.71

(b) what is the ground speed of the plane? Give your answer correct to 2 decimal places.
Note: Ground speed only takes into account the horizontal components of the velocity of the plane relative to the ground.

and

An airplane is flying at an airspeed of 690 km/hr in a cross-wind that is blowing from the northeast at a speed of 55 km/hr.

In what direction should the plane head to end up going due east? Give your answer correct to 2 decimal places.

Any help is appreciated

Sorry, I wrote a nice little lecture making the mistake described below.

I just figured out this problem. Problem was that for a in part a I was doing 525 + 70.71.

That is wrong because, the airspeed is not the i component of the airplane's velocity vector. The 525 is actually rising out from the xy flat coordinate system, into the z-dimension. So 525 is the hypotenuse, while 80 is one of the sides. 80 is the k component. The i component is then 525^2 - 80^2.

Then it's easy from there once you know the i component.