# 1 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).

We can assume the line joining the origin, be OA where $O(0,0,0)$ and the point $A(2,1,1)$ and PQ be the line joining the points $P(3,5,-1)$ and $Q(4,3,-1)$.

Then the direction ratios of the line OA will be $(2-0),(1-0),\ and\ (1-0) = 2,1,1$  and that of line PQ will be

$(4-3),(3-5),\ and\ (-1+1) = 1,-2,0$

So to check whether line OA is perpendicular to line PQ then,

Applying the relation we know,

$a_{1}a_{2}+b_{1}b_{2}+c_{1}c_{2} = 0$

$\Rightarrow 2(1)+1(-2)+1(0) = 2-2+0 = 0$

Therefore OA is perpendicular to line PQ.

## Related Chapters

### Preparation Products

##### Knockout NEET May 2021

An exhaustive E-learning program for the complete preparation of NEET..

₹ 22999/- ₹ 14999/-
##### Knockout BITSAT 2020

It is an exhaustive preparation module made exclusively for cracking BITSAT..

₹ 4999/- ₹ 1999/-
##### Knockout NEET May 2022

An exhaustive E-learning program for the complete preparation of NEET..

₹ 34999/- ₹ 24999/-
##### Knockout JEE Main April 2021

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 22999/- ₹ 14999/-