The direction ratios of the line, which is equally inclined to the three mutually perpendicular lines with direction cosines l1, m1, n1: l2, m2, n2 : l3, m3, n3; are given bya)l1+m1+n1: l2+m2+n2 : l3+m3+n3b)l1+l2+l3 ; m1+m2+m3; n1+n2+n3c)m1n2-m2n1; n1l2-n2l1; m2-l2m1d)none of the aboveCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Proof: Let the three mutually perpendicular lines be

Answer

Explanation:

To find the direction ratios of the line that is equally inclined to three mutually perpendicular lines, we can use the concept of direction cosines.

Concept:

Direction cosines are the cosines of the angles that a given line makes with the positive directions of the coordinate axes. The direction cosines are denoted by l, m, and n.

Solution:

Let the direction cosines of the three mutually perpendicular lines be l1, m1, n1; l2, m2, n2; and l3, m3, n3.

We need to find the direction ratios of the line that is equally inclined to these three lines.

The direction ratios of a line are defined as the ratios of the direction cosines.

So, the direction ratios of the line are l1/l2, m1/m2, and n1/n2.

Since the line is equally inclined to all three lines, the direction ratios of the line will be the same as the direction ratios of any one of the given lines.

Therefore, the direction ratios of the line are l1, m1, n1; l2, m2, n2; and l3, m3, n3.

Hence, the correct answer is option 'B': l1 l2 l3 ; m1 m2 m3; n1 n2 n3.

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