Question

The driver of a car travels 10 km, north after that he turned 8 km, east to go to his work. How far he might travel if he take the short cut straight to his work? Express your answer in vector.

Answer 1

If we direct the y-axis along the northern direction and x-axis along the eastern one, then the coordinates of the first part vector will be:

$$\mathbf{d_1} = (0,10) \space [km]$$

The coordinates of the second part vector will be:

$$\mathbf{d_2} = (8,0) \space[km]$$

The short path vector will be:

$$\mathbf{d} = \mathbf{d_1} + \mathbf{d_2} = (0,10) + (8,0) = (8,10) \space[km]$$

The lenght of the short path is:

$$d = |\mathbf{d}| = \sqrt{8^2 + 10^2} \approx 12.8\space km$$

Answer. Vector of the short path: $\mathbf{d} = (8,10) \space[km]$. Length of the short path: $d = 12.8 \space km$.