`u = 3i + 4j, v = -2j` Find the angle theta between the vectors.

You need to use the formula of dot product to find the angle between two vectors, `u = u_x*i + u_y*j, v = v_x*i + v_y*j` , such that:

`u*v = |u|*|v|*cos(theta)`

The angle between the vectors u and v is theta.

`cos theta = (u*v)/(|u|*|v|)`

First, you need to evaluate the product of the vectors u and v, such that:

`u*v = u_x*v_x + u_y*v_y`

`u*v = 3*0 + 4*(-2)`

`u*v = -8`

You need to evaluate the magnitudes |u| and |v|, such that:

`|u|= sqrt(u_x^2 + u_y^2) => |u|= sqrt(3^2 + 4^2) =>|u|= 5 `

`|v|= sqrt(v_x^2 + v_y^2) => |v|= sqrt(0^2 + (-2)^2) => |v|= 2`

`cos theta = (-8)/(2*5) => cos theta = (-4)/(5)`

Hence, the cosine of the angle between the vectors u and v is `cos theta = -4/5` , so, `theta ~~ 143^o.`