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Question
Suppose \[\vec{a}\] is a vector of magnitude 4.5 units due north. What is the vector (a) \[3 \vec{a}\], (b) \[- 4 \vec{a}\] ?
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Solution
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):
\[\left| - 4 \vec{a} \right| = - 4 \times 4.5 = - 18 \text{ units }\]
∴ \[- 4 \vec{a}\] is a vector of magnitude 18 units due south.
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