James loves using online map services to drive. On a drive to a bookshop, he drives north for 4.5 km, then 2.8 km west, and then 1.3 km south. Using the method of components find the magnitude and direction of the resultant displacement.

A particle moving in the wind has a velocity of (17 i - 6j) mph that lasts for 45 min. The wind changes direction affecting the particle velocity. The new velocity is (5i + 18j) mph and lasts for 1.5 h. Calculate the displacement of the particle, giving the result in component form with unit vectors.

For vectors A = 3i + 4j + 5k; B = 4i + 2j + √5 k, what would be the ratio of the magnitude of A to B?

Use vectors M and N as given in the drawing below. Determine P = M + N, giving the result in component form with unit vectors.

Determine the angle θ formed between the given vectors A and B.

A car is moving on a three-dimensional coordinate system, and its velocity is represented by the vector $\overrightarrow{V}$ = (25.0î + 10.0ĵ - 15.0k̂) m/s. Determine the angles that this velocity vector makes with the x, y, and z axes.

Vector $\overline{M}$ lies in the xy plane making an angle of θ above the positive x-axis. Vector $\overline{N}$ is lying in the same plane making an angle Φ below the positive x-axis. Determine their dot product.

Hint: Use one of the following identities-

cos(A + B) = cosAcosB - sinAsinB

cos(A - B) = cosAcosB + sinAsinB

Find the vector magnitude and direction of the vector product M x N for the two vectors below. 

Find the cross product  (E ✕ F ) of the given vectors.