Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XII  >>  Math  >>  Three Dimensional Geometry
0 votes

Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, – 1), (4, 3, – 1).

Can you answer this question?

1 Answer

0 votes
  • If two lines are $\perp$ then the sum of the product of their direction cosines is $0$
  • (i.e) $a_1a_2+b_1b_2+c_1c_2=0$
Step 1:
Let $OA$ be the line joining the origin (0,0,0) and the point $A(2,1,1)$
Let $BC$ be the line joining the points $B(3,5,-1)$ and $(4,3,-1)$
The direction ratios of $OA$ are (2,1,1) and $BC$ are [(4-3),(3-5),(-1+1)]
Step 2:
It is given $OA$ is perpendicular to $BC$
Hence $a_1a_2+b_1b_2+c_1c_2=0$
Substituting for $(a_1,b_1,c_1)$ and $(a_2,b_2,c_2)$ we get
$2\times 1+1\times -2+1\times 0$
$\Rightarrow 2-2+0$
$\Rightarrow 0$
Hence $OA$ is $\perp$ $BC.$
answered Jun 3, 2013 by sreemathi.v

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