Question

Consider the x-axis as representing east, the y–axis as north, and the z-axis as vertically upwards. Give the vector representing each of the following points.

a) 5 m northeast and 2 m up

b) 4 m southeast and 3 m up

c) 2 m northwest and 4 m up

Answer 1

5m northeast and 2m up.

(a) The vector representation of 5m N-E and 2m up is (5i + 5j) Cos 45° + 2${\displaystyle \hat{k}}$

= ${\displaystyle \frac{5(i+j)}{\sqrt{2}}+2\hat{k}}$

 

(b) 4m south east and 3m up.

The vector representing 4m southeast and 3m up is

(4i - 4j) cos 45° + ${\displaystyle \hat{k}}$

${\displaystyle \frac{4(i-j)}{\sqrt{2}}+3\hat{k}}$

(c) 2m north west and 4m up.

The vector representing 2m northwest and 4m up

= (-2i + 2j) cos 45° + 4${\displaystyle \hat{k}}$

= ${\displaystyle \frac{2(-i+j)}{\sqrt{2}}+4\hat{k}}$

= (-i + ${\displaystyle \hat{j}}$)${\displaystyle \sqrt{2}+4\hat{k}}$