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Question
Write the projection of the vector `(vecb + vecc)` on the vector `veca`, where `veca = 2hati - 2hatj + hatk, vecb = hati + 2hatj - 2hatk` and `vecc = 2hati - hatj + 4hatk`.
Solution
Given vectors, `veca = 2hati - 2hatj + hatk`
`vecb = hati + 2hatj - 2hatk`
`vecc = 2hati - hatj + 4hatk`
`vecb + vecc = (hati + 2hatj - 2hatk) + (2hati - hatj + 4hatk)`
or, `vecb + vecc = 3hati + hatj + 2hatk`
Projection of `(vecb + vecc)` on `veca = ((vecb + vecc).veca)/|veca|`
= `((3hati + hatj + 2hatk).(2hati - 2hatj + hatk))/sqrt((2)^2 + (2)^2 + (1)^2)`
= `(6 - 2 + 2)/3`
= 2
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