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In any triangle A B C , prove the projec...

In any triangle `A B C ,` prove the projection formula`a=b cosC+c cosB` using vector method.

Text Solution

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Let ` vecBC=veca, vecCA=vecb, vecAB=vecc`, so that
BC=a, CA =b,AB=c
`Now" " veca+vecb+vecc=vec0`
`veca.(veca+vecb+vecc)=0`
`veca.veca+veca.vecb+vecc=0`
`a^(2)+ab cos ( 180^(@)-C)+ac cos ( 180^(@)-B)=0`
`a-b cosC-c cosB=0`
`a=b cos C +c cos B`
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