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Question
Find the projection of the vector `hat"i" + 3hat"j" + 7hat"k"` on the vector `2hat"i" + 6hat"j" + 3hat"k"`
Solution
The given vectors are `hat"i" + 3hat"j" + 7hat"k"` and `2hat"i" + 6hat"j" + 3hat"k"`
Projection of `hat"i" + 3hat"j" + 7hat"k"` on `2hat"i" + 6hat"j" + 3hat"k"`
= `((hat"i" + 3hat"j" + 7hat"k")*(2hat"i" + 6hat"j" + 3hat"k"))/(|2hat"i" + 6hat"j" + 3hat"k"|)`
= `((1)(2) + (3)(6) + (7)(3))/sqrt(2^2 + 6^2 + 3^2)`
= `(2 + 18 + 21)/sqrt(4 + 36 + 9)`
= `41/sqrt(49)`
= `41/7`
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