Need Help with Physcis

Should be easy, I just need a confirmation on my process and answer before i turn it in.

 Spoiler

Vector A has a magnitude of 6.00 units, vector B has a magnitude if 7.00 units, and A * B has a value of 14.0. What is the angle between the directions of A and B?

Have no idea how to do this...

 Spoiler

In Fig. 3-31(below), a "vector a" with magnitude of 17.0m is directed at angle Theta =56.0 degrees counterclockwise from the +X axis. What are the components (a) ax and (b) ay of the vector? A second coordinate system is inclined by angle Theta1 = 18.0 degrees with respect to the first. What are the componets © a1x and (d) a1y in this primed coordinate system?

thanks in advance

Is the * in the first part supposed to represent a dot product/scalar product? Because you can't just multiply two vectors, lol.
If it is, then its just AdotB=A*B*Cos(theta). Solve for theta [theta = arccos(AdotB/(A*B))]

For part 2, you know the vector a, which you can imagine as being along a Hypotenuse of a triangle. Then ax and ay are the other two sides, how would you use trig functions to find the values for them normally?
parts c and d are the same thing with a shifted co-ordinate system. Just imagine (or redraw it!) to have the x axis now along ax' and the y axis along ay'. Find the new theta between a and ax', and then solve like before

The dot product (a.b)/|b| gives the magnitude of vector a projected on vector b. This is easier to do than changing systems each time.