Physics - Vectors Question with Solution | TestHub

(A) $|\hat{a}+\hat{b}|=\sqrt{|\hat{a}{|}^2+|\hat{b}{|}^2+2\hat{a}\cdot \hat{b}}$

$\left|\frac{\hat{a}+\hat{b}}{\sqrt{3}}\right|=\frac{1}{\sqrt{3}}\sqrt{|\hat{a}{|}^2+|\hat{b}{|}^2+2\hat{a}\cdot \hat{b}}=\frac{1}{\sqrt{3}}\sqrt{1+1+1}=\frac{1}{\sqrt{3}}\sqrt{3}=1$

(B) $|\hat{a}-\hat{b}|=\sqrt{|\hat{a}{|}^2+|\hat{b}{|}^2-2\hat{a}\cdot \hat{b}}$

$|\hat{a}-\hat{b}|=\sqrt{1+1-1}=\sqrt{1}=1$

(C) $|\hat{a}|=1$

(D) $|\hat{b}|=1$