Chapter 4, Problem 4.20P

Solve the following system by graphing and verify that your solution satisfies the system. {2x + y  =  20 {x + y  =  12 (x, y) = ( ? )

Let vector A  point from the origin into the second quadrant of the xy plane and vector B point from the origin into the fourth quadrant. The vector B −A  must be in which quadrant?

Obtain the sine law of plane trigonometry by interpreting the product A × B and the alternate representation (A − B) × B.

Rectangular coordinates of a point are given by (2,y) and its polar coordinates are given by (r,/6) . Find y y and r .

If f is a scalar function and v = [v1, v2, v3] is a vector field. Show that div(fv)=f divv+v·∇f