Question

If \( |\vec{a}| = 3 \), \( |\vec{b}| = 4 \) and \( \vec{a} \cdot \vec{b} = 6 \), then the angle between \( \vec{a} \) and \( \vec{b} \) is:

• A. $30^{\circ}$
• B. $45^{\circ}$
• C. $60^{\circ}$
• D. $90^{\circ}$

Hint:

The dot product is a measure of how much one vector "goes in the direction" of another.

Answer 1

The Correct Option is C

Step 1: Concept
$\vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos \theta$.
Step 2: Analysis
$6 = (3)(4) \cos \theta \Rightarrow 6 = 12 \cos \theta \Rightarrow \cos \theta = 1/2$.
Step 3: Conclusion
$\theta = \cos^{-1}(1/2) = 60^{\circ}$.
Final Answer: (C)