Question

Find the projection of the vector `hati+3hatj+7hatk`  on the vector `2hati-3hatj+6hatk`

Answer 1

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