# Please answer this one with the help of diagram

The given figure help you regarding the solution

the man moves in direction X axis =

$4\hat{i}-\hat{i}-3\sqrt{2}\mathrm{cos}{45}^{0}\hat{i}(angle{45}^{0}becausenorth-westdirectiongiveninquestion)\phantom{\rule{0ex}{0ex}}3\hat{i}-3\sqrt{2}\times \frac{1}{\sqrt{2}}\hat{i}\phantom{\rule{0ex}{0ex}}3\hat{i}-3i=0$

the man moves along Y axis =$4\hat{j}+3\sqrt{2}\mathrm{sin}\theta \hat{j}=4\hat{j}+3\sqrt{2}\mathrm{sin}{45}^{0}\hat{j}=4\hat{j}+3\sqrt{2}\times \frac{1}{\sqrt{2}}\hat{j}=4\hat{j}+3\hat{j}=7\hat{j}$

since the displacement is along Y direction only.

hence magnitude = 7 km along NORTH direction

Regards

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