Question

Hey, I've got vector problems I'm stuck on; someone help me please!!! My question is "Find the projection of v=2i+3j in the direction of w=4i-2j." I don't know what I should do here...... If someone helps me out, please show me how to do it! Thanks!

Answer 1

Hello,


$proj_{\vec{w}} (\vec{v})= \dfrac{\vec{v} \times\vec{w}}{||\vec{w}||^2} * \vec{w}\\\\ =\dfrac{(2*\vec{i}+3*\vec{j})\times(4*\vec{i}-2*\vec{j})}{8} *(4*\vec{i}-2*\vec{j})\\\\ = \dfrac{2}{8} *(4*\vec{i}-2*\vec{j})\\\\ =\vec{i}- \dfrac{\vec{j}}{4}$