Question

If the direction ratios of a line are proportional to 1, –3, 2, the its direction cosines are

A. \(\frac{1}{\sqrt{14}},\frac{-3}{\sqrt{14}},\frac{2}{\sqrt{14}}\)

B. \(\frac{1}{\sqrt{14}},\frac{2}{\sqrt{14}},\frac{3}{\sqrt{14}}\)

C. \(-\frac{1}{\sqrt{14}},\frac{3}{\sqrt{14}},\frac{2}{\sqrt{14}}\)

D. \(-\frac{1}{\sqrt{14}},-\frac{2}{\sqrt{14}},-\frac{3}{\sqrt{14}}\)

Answer 1

The answer is (A)

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If the direction ratios of a line are proportional to 1, –3, 2, then its direction cosines are also proportional to 1, -3, 2

So let directional cosines be x, -3x, 2x

Now, sum of squares of directional cosines = 1 (property)

So, x² + 9x² + 4x² = 1

x² = 1/14

x = +/- \(\frac{1}{\sqrt14}\)

So direction cosines can be +/- (\(\frac{1}{\sqrt14}i - \frac{3}{\sqrt14}j + \frac{2}{\sqrt14}k\))

So the answer is (A)

Hope it helps

Ask if any doubt

Answer 2

Correct answer is A.

The direction ratios of the line are proportional to 1, -3, 2.

The direction cosines of the lines are →