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Vector Algebra

Question
CBSEENMA12034053
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Evaluate the scalar product:
left parenthesis 3 straight a with rightwards arrow on top space minus space 5 space straight b with rightwards arrow on top right parenthesis. space space left parenthesis 2 straight a with rightwards arrow on top plus space 7 straight b with rightwards arrow on top right parenthesis

Solution

Consider left parenthesis 3 straight a with rightwards arrow on top space minus space space 5 straight b with rightwards arrow on top right parenthesis. space left parenthesis 2 straight a with rightwards arrow on top space plus space 7 straight b with rightwards arrow on top right parenthesis
                          equals space 6 space straight a with rightwards arrow on top. space straight a with rightwards arrow on top space plus space 21 space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space minus space 10 space straight b with rightwards arrow on top. space straight a with rightwards arrow on top space minus space 35 space straight b with rightwards arrow on top. space straight b with rightwards arrow on top
                           equals space 6 space straight a with rightwards arrow on top squared space plus 21 space straight a with rightwards arrow on top semicolon space straight b with rightwards arrow on top space minus space 10 space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space minus 35 space straight b with rightwards arrow on top squared space equals 6 space open vertical bar straight a with rightwards arrow on top close vertical bar squared space plus space 11 space straight a with rightwards arrow on top. space space straight b with rightwards arrow on top space minus space 35 space open vertical bar straight b with rightwards arrow on top close vertical bar squared space space space space space space space space space space space space space space space space space space space open square brackets because space straight a with bar on top. space straight b with bar on top space equals space straight b with bar on top. space straight a with bar on top close square brackets

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