Question

two vector have a magnitude F and 2root F .they are inclined to each other at an angle of 135 degree .find their resultant in magnitude and direction .how to I solve it

Answer 1

$$R=\sqrt{F^2+(\sqrt{2}F)^2+2F\sqrt{2}F\cos{135}}$$

$$R=\sqrt{1+2-2\sqrt{2}\cos{45}}F=F$$

For direction you should have to use this formula

$$\tan{\alpha}=\frac{F\sin{135}}{F\cos{135}+F}=\frac{\sin{135}}{\cos{135}+\sqrt{2}}$$

$$\alpha=45\degree$$