What is the angle between \( \vec{a} \) and \( \vec{c} \) ?

For the next two (02) items that follow : Let \( \vec{a}, \vec{b}, \vec{c}, \vec{a}+\vec{b}, \vec{b}+\vec{c}, \vec{a}+\vec{b}+\vec{c} \) be unit vectors.

  1. A. \frac{\pi}{6}
  2. B. \frac{\pi}{4}
  3. C. \frac{\pi}{2} ✓
  4. D. \frac{2\pi}{3}

Correct Answer: C. \frac{\pi}{2}

Explanation

Expanding |a+b+c|^2 = 1 yields |a|^2 + |b|^2 + |c|^2 + 2(a.b + b.c + c.a) = 1. We know a.b = -1/2 and b.c = -1/2. Substituting these gives 3 + 2(-1 + c.a) = 1, leading to c.a = 0. Hence, the angle is \pi/2.

Related questions on Vector Algebra

Practice more NDA Mathematics questions