Question

Let \( \vec{u}, \vec{v} \) and \( \vec{w} \) be vectors such that \( \vec{u} + \vec{v} + \vec{w} = \vec{0} \). If \( |\vec{u}| = 3, |\vec{v}| = 4 \) and \( |\vec{w}| = 5 \) then \( \vec{u} \cdot \vec{v} + \vec{v} \cdot \vec{w} + \vec{w} \cdot \vec{u} = \)

• A. \( 0 \)
• B. \( -25 \)
• C. \( 25 \)
• D. \( 50 \)
• E. \( 47 \)

Hint:

This problem is essentially finding the sum of the products of sides in a triangle. Since \( 3, 4, 5 \) is a Pythagorean triplet, these vectors actually form a right-angled triangle.

Answer 1

The Correct Option is B