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Home  >>  TN XII Math  >>  Vector Algebra

Find the magnitude of $\overrightarrow{a} \times \overrightarrow{b}$ if $\overrightarrow{a}=\overrightarrow{2i}+\overrightarrow{k}, \overrightarrow{b}=\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}$

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  • If $ \overrightarrow a = a_1\overrightarrow i+a_2\overrightarrow j+a_3\overrightarrow k, \: \overrightarrow b = b_1\overrightarrow i+b_2\overrightarrow j+b_3\overrightarrow k$ then $ \overrightarrow a$ x $ \overrightarrow b = \begin{vmatrix} \overrightarrow i & \overrightarrow j & \overrightarrow k \\ a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \end{vmatrix}$
$ \overrightarrow a $ x $ \overrightarrow b = \begin{vmatrix} \overrightarrow i & \overrightarrow j & \overrightarrow k \\ 2 & 0 & 1 \\ 1 & 1 & 1 \end{vmatrix} = (0-1)\overrightarrow i-(2-1)\overrightarrow j+(2-0)\overrightarrow k$
$ = -\overrightarrow i-\overrightarrow j+2\overrightarrow k$
$ |\overrightarrow a$ x $ \overrightarrow b| = \sqrt{1+1+4}= \sqrt 6$
answered Jun 5, 2013 by thanvigandhi_1
 

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