How would you express B⃗ using unit vectors? Express your answers in terms of the unit vectors x^ and y^. Use the unit vector button under the templates menu in the answer box to create unit vectors.

B = B (cos θ  x ^ + sin θ  y ^)

Explanation:

To represent the magnetic field B using unit vectors, the magnitude of the field and the angle with respect to some coordinate axis must be known. Having this information, trigonometry can be used.

Suppose that the angle we have is with respect to the positive side of the x-axis, let's use trigonometry

             cos θ = Bₓ / B

             sin θ = / B

             Bx = B cos θ

             B_{y} = B sin θ

so the resulting vector is

             B = Bₓ i ^ + B_{y} j ^

unit vectors

             x ^ = i ^

             y ^ = j ^

let's write the complete answer

          B = B (cos θ  x ^ + sin θ  y ^)

The bold indicate vector

d is the correct answer

no. dot product   =0 when vecs at right angles