If , , , then show that a a ' + b b ' + c c ' = 0, where a , b and c are…

MATHEMATICS · Subjective · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

If a′=b×c[abc]\mathbf{a}' = \frac{\mathbf{b} \times \mathbf{c}}{[\mathbf{a} \mathbf{b} \mathbf{c}]} , b′=c×a[abc]\mathbf{b}' = \frac{\mathbf{c} \times \mathbf{a}}{[\mathbf{a} \mathbf{b} \mathbf{c}]} , c′=a×b[abc]\mathbf{c}' = \frac{\mathbf{a} \times \mathbf{b}}{[\mathbf{a} \mathbf{b} \mathbf{c}]} , then show that a×a′+b×b′+c×c′=0, where a,b and c are non-coplanar.\mathbf{a} \times \mathbf{a}' + \mathbf{b} \times \mathbf{b}' + \mathbf{c} \times \mathbf{c}' = 0, \text{ where } \mathbf{a}, \mathbf{b} \text{ and } \mathbf{c} \text{ are non-coplanar.}

Related theory

Browse the problem library