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Find the (i) Scalar component and (ii)ve...

Find the (i) Scalar component and (ii)vector component of `A=3hati+4hatj+5hatk on B=hati+hatj+hatk.`

Text Solution

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(i) Scalar component of a A along B is
`Acostheta=A.hatB=(3hati+4hatj+5hatk).((hati+hatj+hatk))/(sqrt(3))`
` =(3+4+5)/(sqrt(3))=(12)/(sqrt(3))=4sqrt(3)`
(ii) Vector component of A along B is
`(Acostheta)hatB=(A.hatB)hatB`
`(4sqrt(3))((hati+hatj+hatk))/(sqrt(3))=4hati+ 4hatj+4hatk`
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