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Q. If $ |\overrightarrow{a}|=6,|\overrightarrow{b}|=8,|\overrightarrow{a}-\overrightarrow{b}|=10, $ then $ |a+b| $ is equal to:

KEAMKEAM 2001

Solution:

$ \because $ $ |\overrightarrow{a}-\overrightarrow{b}{{|}^{2}}={{\overrightarrow{a}}^{2}}+{{\overrightarrow{b}}^{2}}-2\overrightarrow{a}.\overrightarrow{b} $ $ \Rightarrow $ $ 100=36+64-2\overrightarrow{a}.\overrightarrow{b} $ $ \Rightarrow $ $ \overrightarrow{a}.\overrightarrow{b}=0 $ $ \therefore $ $ |\overrightarrow{a}+\overrightarrow{b}{{|}^{2}}={{\overrightarrow{a}}^{2}}+{{\overrightarrow{b}}^{2}}+2\overrightarrow{a}.\overrightarrow{b} $ $ =36+64+0=100 $ $ \Rightarrow $ $ |\overrightarrow{a}+\overrightarrow{b}|=10 $