Question

If a➝ , b➝ and c➝ are three unit vectors such that
a➝ + b➝ + c➝ = 0 than the value of a➝ . b➝ + b➝ . c➝ + c➝ . a➝ is
(a) 3 (b) –1
2
(c) 0 (d) – 3
2

Answer 1

Answer

-3/2.

Explanation Given above.

Answer 2

First know about some properties of Scalar product :

1) scalar product is commutative.

$\vec{A}.\vec{B} =\vec{B}.\vec{ A}$

2) scalar product is distributed over addition.

$\vec{A}.( \vec{B}+ </p><p>\vec{ C} ) = \vec{A} .\vec{B}+\vec{A} .\vec{C }$

3) $\vec{A}.0= O$

4) $\vec{a}. \vec{a}= 1$

Solution :

$\vec{A}.\vec{B}+ </p><p>\vec{B}.\vec{ C} +\vec{C} .\vec{A}= \frac{-3}{2}$