Vector Algebra
Angle Between Vectors
Grade 12
Question:
<p>The non-zero vectors <strong>a</strong>, <strong>b</strong> and <strong>c</strong> are related by <strong>a</strong> = 8<strong>b</strong> and <strong>c</strong> = -7<strong>b</strong>. Find the angle between <strong>a</strong> and <strong>c</strong>.</p>
<p>(a) \(\frac{\pi}{4}\)</p>
<p>(b) \(\frac{\pi}{2}\)</p>
<p>(c) \(\pi\)</p>
<p>(d) 0</p>
Step-by-Step Solution
Key Concept: When a vector is multiplied by a positive scalar, direction remains the same; by a negative scalar, direction reverses. Opposite direction vectors make angle π.
Solution: Since a = 8 b , vectors a and b are in the same direction. Since c = -7 b , vectors b and c are in opposite directions. Therefore, a and c are in opposite directions. ∴ The angle between a and c is \(\pi\).
Correct Answer: C