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Vector Algebra

Question
CBSEENMA12034146
Wired Faculty App

Prove that in any triangle ABC, c = a cos B + b cos A.

Solution

Let BC with rightwards arrow on top space equals straight a comma space space CA with rightwards arrow on top space equals space straight b with rightwards arrow on top
   AB with rightwards arrow on top space equals straight c with rightwards arrow on top space so space that BC space equals space straight a comma space space space CA space equals space straight b comma space space AB space equals space straight c
Now,   straight a with rightwards arrow on top plus straight b with rightwards arrow on top plus straight c with rightwards arrow on top space equals space 0 with rightwards arrow on top
rightwards double arrow space space straight c with rightwards arrow on top. space left parenthesis straight a with rightwards arrow on top plus straight b with rightwards arrow on top plus straight c with rightwards arrow on top right parenthesis space equals space 0 rightwards double arrow space space straight c with rightwards arrow on top. space straight a with rightwards arrow on top space plus space straight c with rightwards arrow on top. space straight b with rightwards arrow on top space plus space straight c with rightwards arrow on top. space straight c with rightwards arrow on top space equals space 0 space space space space space space space space straight c space straight a space cos space left parenthesis 180 degree minus straight A right parenthesis space plus space straight c space straight b space cos space left parenthesis 180 degree space minus space straight B right parenthesis space plus space straight c squared space equals space 0 rightwards double arrow space space space minus straight c space straight a space cos space straight B space minus space straight c space straight b space cos space straight A space plus straight c squared space equals space 0 rightwards double arrow space space space space minus space straight a space cos space straight B space minus space straight b space cos space straight A space equals space minus straight c therefore space space space space space space space straight c space equals space straight a space cos space straight B space plus space straight b space cos space straight A

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