91Ó°ÊÓ

A vector is a physical quantity that has both magnitude and direction. The vector can be split into two or more scalar components when added, producing the same effect as it produced by a single vector.

The north component of displacement from San Francisco to Sacramento is

$s_n=S\sin (45°)$

Here S is the magnitude of the displacement.

Substitute 123 km for S.

$$\begin{gathered} s_n=123km×\sin 45° \\ =86.97km \end{gathered}$$

Hence, the north component of the displacement from San Francisco to Sacramento is 86.97km.

The east component of displacement from San Francisco to Sacramento is

$s_E=S\cos (45°)$

Here S is the magnitude of the displacement.

Substitute 123km for S .

$$\begin{gathered} S_E=123km×\cos (45°) \\ =86.97km \end{gathered}$$

Hence, the east component of the displacement from San Francisco to Sacramento is 86.97km.