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Question Number 45876 by rahul 19 last updated on 17/Oct/18

Answered by tanmay.chaudhury50@gmail.com last updated on 17/Oct/18

$$\mid \overrightarrow{a}+\overrightarrow{b}\mid =\sqrt{29}$$$$\overrightarrow{a}\times \overrightarrow{c}=\overrightarrow{c}\times \overrightarrow{b}$$$$\overrightarrow{a}\times \overrightarrow{c}=-\overrightarrow{b}\times \overrightarrow{c}$$$$(\overrightarrow{a}+\overrightarrow{b})\times \overrightarrow{c}=0$$$$so(\overrightarrow{a}+\overrightarrow{b})=2\lambda i+3\lambda j+4\lambda k$$$$\mid (\overrightarrow{a}+\overrightarrow{b})\mid =\sqrt{4{\lambda }^2+9{\lambda }^2+16{\lambda }^2}=\sqrt{29}\lambda =\sqrt{29}$$$$so\lambda =1$$$$(\overrightarrow{a}+\overrightarrow{b})=2i+3j+4k$$$$(\overrightarrow{a}+\overrightarrow{b}).(-7i+2j+3k)$$$$=(2i+3j+4k).(-7i+2j+3k)$$$$=2\times -7+3\times 2+4\times 3$$$$=-14+6+12=4$$

Commented by rahul 19 last updated on 18/Oct/18

$$thankssir.$$

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