Question

Two vectors $ \overrightarrow{a} $ and $ \overrightarrow{b} $ of equal magnitude 5 originating from a point and directs respectively towards north-east and north-west. Then the magnitude of $ \vec{a}-\vec{b} $ is:

• A. $ 3\sqrt{2} $
• B. $ 2\sqrt{3} $
• C. $ 2\sqrt{5} $
• D. $ 5\sqrt{2} $
• E. $ 5\sqrt{3} $

Answer 1

Answer: (D)

$ |\overrightarrow{a}-\overrightarrow{b}{{|}^{2}}=|\overrightarrow{a}{{|}^{2}}+|\overrightarrow{b} {{|}^{2}}-2|\overrightarrow{a}||\overrightarrow{b}|\cos 90{}^\circ $
$ =25+25-2\times 0 $
$ =50 $
$ \Rightarrow $ $ |\overrightarrow{a}-\overrightarrow{b}|=5\sqrt{2} $