Question and Answers Forum

All Questions      Topic List

Vector Questions

Previous in All Question      Next in All Question      

Previous in Vector      Next in Vector      

Question Number 42521 by rahul 19 last updated on 27/Aug/18

$$\mathrm{Let}\overrightarrow{\mathrm{a}},\overrightarrow{\mathrm{b}},\overrightarrow{\mathrm{c}}\mathrm{be}\mathrm{three}\mathrm{unit}\mathrm{vectors}$$$$\mathrm{such}\mathrm{that}3\overrightarrow{\mathrm{a}}+4\overrightarrow{\mathrm{b}}+5\overrightarrow{\mathrm{c}}=0.\mathrm{Then}\mathrm{prove}$$$$\mathrm{that}\overrightarrow{\mathrm{a}},\overrightarrow{\mathrm{b}},\overrightarrow{\mathrm{c}}\mathrm{are}\mathrm{coplanar}.$$

Answered by tanmay.chaudhury50@gmail.com last updated on 27/Aug/18

$$wehavetoprove\left(\overrightarrow{a}\times \overrightarrow{b}\right).\overrightarrow{c}=0$$$$3\overrightarrow{a}+5\overrightarrow{c}=-4\overrightarrow{b}$$$$(3\overrightarrow{a}+5\overrightarrow{c})\times \overrightarrow{b}=-4\overrightarrow{b}\times \overrightarrow{b}$$$$3\overrightarrow{a}\times \overrightarrow{b}+5\overrightarrow{c}\times \overrightarrow{b}=0$$$$3\overrightarrow{a}\times \overrightarrow{b}=-5\overrightarrow{c}\times \overrightarrow{b}$$$$3\left(\overrightarrow{a}\times \overrightarrow{b}\right).\overrightarrow{c}=-5\left(\overrightarrow{c}\times \overrightarrow{b}\right).\overrightarrow{c}$$$$hence$$$$3\left(\overrightarrow{a}\times \overrightarrow{b}\right).\overrightarrow{c}=0so\left(\overrightarrow{a}\times \overrightarrow{b}\right).\overrightarrow{c}=0$$$$hdnceproved$$$$$$$$$$

Commented by rahul 19 last updated on 31/Aug/18

thanks sir.

Terms of Service

Privacy Policy

Contact: info@tinkutara.com