# Compute the magnitude of the following vectors: $(iii)\;\overrightarrow c = \large\frac{1}{\sqrt 3}$$\hat i +\large \frac{1}{\sqrt 3}$$\hat j - \large\frac{1}{\sqrt 3}$$\hat k This question has multiple parts. Therefore each part has been answered as a separate question on Clay6.com ## 1 Answer Toolbox: • The distance between the initial point and the terminal point of a vector is the magnitude (or length) of the vector \overrightarrow{AB}.It is denoted by \mid\overrightarrow{AB}\mid or simply AB. • \mid\overrightarrow{AB}\mid=\sqrt{a_1^2+a_2^2+a_3^2} • Where \overrightarrow{AB}=a_1\hat i+a_2\hat j+a_3\hat k. Step 1: \overrightarrow c = \large\frac{1}{\sqrt 3}$$\hat i +\large \frac{1}{\sqrt 3}$$\hat j - \large\frac{1}{\sqrt 3}$$\hat k$
Here $a_1=\large\frac{1}{\sqrt{3}}$$,a_2=\large\frac{1}{\sqrt{3}} and a_3=-\large\frac{1}{\sqrt{3}} \mid \overrightarrow{c}\mid=\sqrt{a_1^2+a_2^2+a_3^2} Step 2: Hence \mid\overrightarrow{c}\mid=\sqrt{\big(\large\frac{1}{\sqrt{3}}\big)^2+\big(\large\frac{1}{\sqrt{3}}\big)^2+\big(-\large\frac{1}{\sqrt{3}}\big)^2} \qquad\qquad=\sqrt{\large\frac{1}{3}+\large\frac{1}{3}+\large\frac{1}{3}}=\large\sqrt{\frac{3}{3}}$$=1$
$\mid\overrightarrow{c}\mid=1$