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Multiplication with Vectors

Suppose a → i...

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):
$3 |\vec{a}| = 3 \times 4.5 = 13.5$
∴ $3 \vec{a}$ is a vector of magnitude 13.5 units due north.

Case (b):
$|- 4 \vec{a}| = 4 \times 1.5 = 6 units$
∴ $- 4 \vec{a}$ is a vector of magnitude 6 units due south.

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Suppose $\to a$ is a vector of magnitude 4.5 unit due north. What is the vector (a) 3 $\to a$ , (b) -4 $\to a$ ?

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