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Question Number 42199 by rahul 19 last updated on 20/Aug/18

Answered by tanmay.chaudhury50@gmail.com last updated on 20/Aug/18

$$a)\left\{(\mathit{a}+\mathit{b})\times (\mathit{b}+\mathit{c})\right\}.(\mathit{c}+\mathit{a})$$$$(\mathit{a}\times \mathit{b}+\mathit{a}\times \mathit{c}+\mathit{b}\times \mathit{b}+\mathit{b}\times \mathit{c}).(\mathit{c}+\mathit{a})$$$$\left(\mathit{a}\times \mathit{b}\right).\mathit{c}+\left(\mathit{b}\times \mathit{c}\right).\mathit{a}=2v$$$$\left[abc\right]=\left[bca\right]=\left[cab\right]=v$$$$b)\left\{(\mathit{a}-\mathit{b})\times (\mathit{b}+\mathit{c})\right\}.(\mathit{c}+\mathit{a})$$$$(\mathit{a}\times \mathit{b}+\mathit{a}\times \mathit{c}-\mathit{b}\times \mathit{c}).(\mathit{c}+\mathit{a})$$$$=\left(\mathit{a}\times \mathit{b}\right).\mathit{c}-\left(\mathit{b}\times \mathit{c}\right).\mathit{a}=0$$$$\mathit{c})\left\{(\mathit{a}+\mathit{b})\times (\mathit{b}-\mathit{c})\right\}.(\mathit{c}+\mathit{a})$$$$=(\mathit{a}\times \mathit{b}-\mathit{a}\times \mathit{c}-\mathit{b}\times \mathit{c}).(\mathit{c}+\mathit{a})$$$$=\left(\mathit{a}\times \mathit{b}\right).\mathit{c}-\left(\mathit{b}\times \mathit{c}\right).\mathit{a}=0$$$$\mathit{d})\left\{(\mathit{a}+\mathit{b})\times (\mathit{b}+\mathit{c})\right\}.(\mathit{c}-\mathit{a})$$$$=(\mathit{a}\times \mathit{b}+\mathit{a}\times \mathit{c}+\mathit{b}\times \mathit{c}).(\mathit{c}-\mathit{a})$$$$=\left(\mathit{a}\times \mathit{b}\right).\mathit{c}-\left(\mathit{b}\times \mathit{c}\right).\mathit{a}=0$$$$\mathit{s}ooptionb,canddvolumezerosocoplaner$$$$$$

Commented by rahul 19 last updated on 20/Aug/18

thanks sir ��

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