What is the value of (p + q) ?

For the next two (02) items that follow : Let \( \vec{a}, \vec{b}, \vec{c} \) be unit vectors. Further, \( \vec{a} \) is perpendicular to \( \vec{b} \); \( \vec{c} \) makes an angle \( \frac{\pi}{3} \) with both \( \vec{a} \) and \( \vec{b} \); and \( \vec{c} = p\vec{a} + q\vec{b} + r(\vec{a} \times \vec{b}) \).

  1. A. \frac{1}{2}
  2. B. 1 ✓
  3. C. \frac{3}{2}
  4. D. 2

Correct Answer: B. 1

Explanation

Taking the dot product of \vec{c} with \vec{a} yields p = \vec{c}\cdot\vec{a} = cos(\pi/3) = 1/2. Taking the dot product with \vec{b} yields q = \vec{c}\cdot\vec{b} = cos(\pi/3) = 1/2. Thus, p + q = 1.

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