$Two vectors of equal magnitude 5 unit have an angle 60° them. Find the magnitude of \left(a\right) the sum of the vectors and \left(b\right) the dlfference of the vectors.$

Dear Student,

Please find below the solution of your asked query:

2.2 (a) $\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}$ is the sum of $\overrightarrow{\mathrm{A}} \mathrm{and} \overrightarrow{\mathrm{B}}$ both have a magnitude of 5 and the angle between them is 60^o. Thus the magnitude of the sum is :

$$\begin{gathered} \left|\begin{array}{cc}\overrightarrow{\mathrm{A}} +& \overrightarrow{\hspace{0.17em}\mathrm{B}}\end{array}\right| = \sqrt{5^2+5^2+2\times 5\times 5 \cos 60°} \\ =2\times 5 \cos 30° \\ =\mathbf{5}\sqrt{\mathbf{3}}\mathbf{ }\mathbf{unit} \end{gathered}$$

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