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Question
Find the projection of the vector `hati+3hatj+7hatk` on the vector `2hati-3hatj+6hatk`
Solution
Let `veca=hati+3hatj+7hatk and vecb=2hati-3hatj+6hatk`
We know that, the projection of a vector `veca ` on another vector `vecb ` is given by `(veca.vecb)/|vecb|`
Now, we have:
`veca.vecb=(hati+3hatj+7hatk).(2hati-3hatj+6hatk)`
`veca.vecb=2-9+42=35`
now, `|vecb|=sqrt(2^2+(-3)^2+6^2)=sqrt(4+9+36)=sqrt49=7`
`(veca.vecb)/|vecb|=35/7=5`
Hence, the projection of `veca=hati+3hatj+7hatk ` on `vecb=2hati-3hatj+6hatk` is 5
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