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If $\overrightarrow{a} =\overrightarrow{i} + \overrightarrow{j}+\overrightarrow{2k}\; and\; \overrightarrow{b}=\overrightarrow{3i} +\overrightarrow{2j}-\overrightarrow{k}$ find $(\overrightarrow{a}+\overrightarrow{3b}) . (\overrightarrow{2a}-\overrightarrow{b})$

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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.\overrightarrow b = a_1b_1+a_2b_2+a_3b_3$
Step 1
$ \overrightarrow a+3\overrightarrow b = \overrightarrow i+\overrightarrow j+2\overrightarrow k+9\overrightarrow i+6\overrightarrow j-3\overrightarrow k = 10\overrightarrow i+7\overrightarrow j-\overrightarrow k$
$2\overrightarrow a-\overrightarrow b=2\overrightarrow i+2\overrightarrow j+4\overrightarrow k-3\overrightarrow i-2\overrightarrow j+\overrightarrow k=-\overrightarrow i+5\overrightarrow k$
Step 2
$(\overrightarrow a+3\overrightarrow b).(2\overrightarrow a-\overrightarrow b)=(10)(-1)+(7)(0)+(-1)(5)=-10-5=-15$
answered May 31, 2013 by thanvigandhi_1

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