Writhe the projection of the vector `7 hat i+ hat j-4 hat k` on the vector `2 hat i+6 hat j+3 hat kdot`

Explanation

Projection of `vec{a} on vec{b}=frac{vec{a} cdot vec{b}}{|vec{b}|}`


`vec{a}=7 hat{i}+hat{j}-4 hat{k} and vec{b}=2 hat{i}+6 hat{j}+3 hat{k}`


Hence,


`vec{a} cdot vec{b}=(7 hat{i}+hat{j}-4 hat{k}) cdot(2 hat{i}+6 hat{j}+3 what{k})=14+6-12=8`


`|vec{b}|=sqrt{2^{2}+6^{2}+3^{2}}=7`


`projection of vec{a} on vec{b}=frac{8}{7}`