Question

Suppose \[\vec{a}\] is a vector of magnitude 4.5 units due north. What is the vector (a) \[3 \vec{a}\], (b) \[- 4 \vec{a}\] ?

Answer 1

Given: \[\vec{a}\] is a vector of magnitude 4.5 units due north.

Case (a):
\[3\left| \vec{a} \right| = 3 \times 4 . 5 = 13 . 5\]

∴ \[3 \vec{a}\] is a vector of magnitude 13.5 units due north.

Case (b):
\[\left| - 4 \vec{a} \right| = 4 \times 1 . 5 = 6 \text{ units }\]

∴ \[- 4 \vec{a}\] is a vector of magnitude 6 units due south.