Question

Q. If the magnitude of resultant of two unequal vectors is equal to the sum of their magnitude. Find the angle between the vectors.

Answer 1

$$\begin{gathered} \mathrm{Let}\stackrel{\rightharpoonup }{a}\mathrm{and}\stackrel{\rightharpoonup }{b}\mathrm{be}\mathrm{two}\mathrm{unequal}\mathrm{vectors}\mathrm{and}\theta \mathrm{be}\mathrm{the}\mathrm{angle}\mathrm{between}\mathrm{them}. \\ \mathrm{Therefore},\mathrm{according}\mathrm{to}\mathrm{question}, \\ \left|\stackrel{\rightharpoonup }{\mathrm{a}}+\stackrel{\rightharpoonup }{\mathrm{b}}\right|=\left|\stackrel{\rightharpoonup }{\mathrm{a}}\right|+\left|\stackrel{\rightharpoonup }{\mathrm{b}}\right| \\ \sqrt{a^2+b^2+2ab\cos \theta }=a+b \\ \Rightarrow {\left(\sqrt{a^2+b^2+2ab\cos \theta }\right)}^2={\left(a+b\right)}^2 \\ \Rightarrow a^2+b^2+2ab\cos \theta =a^2+b^2+2ab \\ \Rightarrow 2ab\cos \theta =2ab \\ \Rightarrow \cos \theta =1 \\ \Rightarrow \cos \theta =\cos 0° \\ \therefore \theta =0° \end{gathered}$$