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Vector Algebra

Question
CBSEENMA12034085
Wired Faculty App

Prove that open vertical bar straight a with rightwards arrow on top close vertical bar space straight b with rightwards arrow on top space plus space open vertical bar straight b with rightwards arrow on top close vertical bar space straight a with rightwards arrow on top is orthogonal to open vertical bar straight a with rightwards arrow on top close vertical bar space straight b with rightwards arrow on top space minus space open vertical bar straight b with rightwards arrow on top close vertical bar space straight a with rightwards arrow on top, for any vectors straight a with rightwards arrow on top space and space straight b with rightwards arrow on top.

Solution
left parenthesis open vertical bar straight a with rightwards arrow on top close vertical bar space straight b with rightwards arrow on top space plus space open vertical bar straight b with rightwards arrow on top close vertical bar space straight a with rightwards arrow on top right parenthesis. space space open parentheses open vertical bar straight a with rightwards arrow on top close vertical bar space straight b with rightwards arrow on top space minus space open vertical bar straight b with rightwards arrow on top close vertical bar space straight a with rightwards arrow on top close parentheses
                               equals space open vertical bar straight a with rightwards arrow on top close vertical bar squared space straight b with rightwards arrow on top squared space minus space open vertical bar straight b with rightwards arrow on top close vertical bar squared space straight a with rightwards arrow on top squared space equals space open vertical bar straight a with rightwards arrow on top close vertical bar squared space open vertical bar straight b with rightwards arrow on top close vertical bar squared space minus space open vertical bar straight b with rightwards arrow on top close vertical bar squared space open vertical bar straight a with rightwards arrow on top close vertical bar squared equals space open vertical bar straight a with rightwards arrow on top close vertical bar squared space open vertical bar straight b with rightwards arrow on top close vertical bar squared space minus space open vertical bar straight a with rightwards arrow on top close vertical bar squared space open vertical bar straight b with rightwards arrow on top close vertical bar squared space equals space 0
therefore space space space space space open vertical bar straight a with rightwards arrow on top close vertical bar space straight b with rightwards arrow on top space plus space open vertical bar straight b with rightwards arrow on top close vertical bar space straight a with rightwards arrow on top space and space open vertical bar straight a with rightwards arrow on top close vertical bar space straight b with rightwards arrow on top space minus space open vertical bar straight b with rightwards arrow on top close vertical bar space straight a with rightwards arrow on top space are space orthozonal space for space any space vectors space straight a with rightwards arrow on top space and space straight b with rightwards arrow on top.

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