Question

If a, b, c are unit vectors such that $\mathbf { a } + \mathbf { b } + \mathbf { c } = \mathbf { 0 }$ then $\mathbf { a } \cdot \mathbf { b } + \mathbf { b } \cdot \mathbf { c } + \mathbf { c } \cdot \mathbf { a } =$

• A. 1
• B. 3
• C. – 3/2
• D. 3/2

Answer 1

Answer: (C)

– 3/2

Answer 2

Squaring $( \mathbf { a } + \mathbf { b } + \mathbf { c } ) = \mathbf { 0 }$

we get $\mathbf { a } ^ { 2 } + \mathbf { b } ^ { 2 } + \mathbf { c } ^ { 2 } + 2 \mathbf { a } \cdot \mathbf { b } + 2 \mathbf { b } \cdot \mathbf { c } + 2 \mathbf { c } \cdot \mathbf { a } = 0$

⇒

⇒ .