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  • 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).

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).

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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.

Posted by

Divya Prakash Singh

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