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Question Number 132650 by aupo14 last updated on 15/Feb/21

Commented by mr W last updated on 15/Feb/21

$$whatdoyoumeanwith\mathit{A}\mathbf{\&}\mathit{B}?$$

Commented by aupo14 last updated on 15/Feb/21

Commented by mr W last updated on 15/Feb/21

$$whatisthat?$$

Commented by mr W last updated on 15/Feb/21

$$iknow$$$$\mathit{A}+\mathit{B}$$$$\mathit{A}-\mathit{B}$$$$\mathit{A}\bullet \mathit{B}$$$$\mathit{A}\times \mathit{B}$$$$buthowis\mathit{A}\mathbf{\&}\mathit{B}defined?$$

Commented by aupo14 last updated on 15/Feb/21

Answered by mr W last updated on 15/Feb/21

Commented by mr W last updated on 16/Feb/21

$$a=\frac{\mathit{A}\cdot \mathit{B}}{\mid \mathit{A}\mid }$$$$\mathit{C}=-\frac{a\mathit{A}}{\mid \mathit{A}\mid }+\mathit{B}=-\frac{\mathit{A}\cdot \mathit{B}}{\mid \mathit{A}{\mid }^2}\mathit{A}+\mathit{B}$$$$=-\frac{1\times 1+1\times (-1)+1\times (-1)}{1^2+1^2+1^2}(1,1,1)+(1,-1,-1)$$$$=(\frac{1}{3},\frac{1}{3},\frac{1}{3})+(1,-1,-1)$$$$=(\frac{4}{3},-\frac{2}{3},-\frac{2}{3})$$$$generally$$$$(2p,-p,-p)issuchavector$$$$withp\in R\wedge p\ne 0$$

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