Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Vector Algebra
0 votes

If $\overrightarrow a, \:\overrightarrow b,\: \overrightarrow c$ are position vectors of the points $A,B,C$ respectively, then under what condition the three points $A,B,C$ are collinear?

$\begin{array}{1 1} \overrightarrow a\times\overrightarrow b=0 \\ \overrightarrow a\times\overrightarrow b \;is\; \parallel \;to \;\overrightarrow b\times\overrightarrow c \\ \overrightarrow a\times\overrightarrow b\; is \;\perp \overrightarrow b\times\overrightarrow c \\ \overrightarrow a\times\overrightarrow b+\overrightarrow b\times\overrightarrow c+\overrightarrow c\times\overrightarrow a=0 \end{array} $

Can you answer this question?

1 Answer

0 votes
  • Two collinear vectors are parallel vectors.
If $A,B,C$ are collinear, then $\overrightarrow {AB}$ is || to $\overrightarrow {AC}$
$\Rightarrow\:(\overrightarrow b-\overrightarrow a)\times(\overrightarrow c-\overrightarrow a)=0$
$\Rightarrow\:\overrightarrow b\times\overrightarrow c+\overrightarrow a\times\overrightarrow b+\overrightarrow c\times\overrightarrow a=0$
answered Nov 10, 2013 by rvidyagovindarajan_1
edited Nov 29, 2013 by rvidyagovindarajan_1

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App