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The direction ratios of the line perpendicular to the lines with direction ratios < 1, -2, -2 > and < 0,2,1 > are
  • a)
    < 2 , - 1 , 2 >
  • b)
    < - 2 , 1 , 2 >
  • c)
    < 2 , l , - 2 >
  • d)
    < - 2 , - 1 , - 2 >
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The direction ratios of the line perpendicular to the lines with direc...
Let the direction ratio be <a, b, c>
Fromeq. (1)&(2)
a = - 2b; c = - 2b 
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Most Upvoted Answer
The direction ratios of the line perpendicular to the lines with direc...
Let the direction ratios of the line be $(a,b,c)$.

For two lines to be perpendicular, their direction ratios must satisfy the condition that their dot product is equal to 0.

So, if the direction ratios of the first line are $(p,q,r)$, we have:

$(p,q,r) \cdot (a,b,c) = 0$

Expanding this, we get:

$pa + qb + rc = 0$

This equation relates the direction ratios of the line perpendicular to the given line. However, there are infinitely many such lines, since any multiple of $(a,b,c)$ will also be perpendicular to the given line.

So, the direction ratios of the line perpendicular to the line with direction ratios $(p,q,r)$ are all multiples of $(p,q,r)$.
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