If a line has the direction ratios –18, 12, –4, then what are its direction cosines?

Mathematics Part-II

Book: Mathematics Part-II

Chapter: 11. Three Dimensional Geometry

Subject: Maths - Class 12^th

Q. No. 3 of Exercise 11.1

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If a line has the direction ratios –18, 12, –4, then what are its direction cosines?

If the direction ratios of the line are a, b and c

Then the direction cosines are

Given direction ratios are – 18, 12 and – 4

⇒ a= -18, b = 12 and c= -4

=

=

Direction cosines are

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Chapter Exercises

Exercise 11.1

Exercise 11.2

Exercise 11.3

Miscellaneous Exercise

1

If a line makes angles 90°, 135°, 45° with the x, y and z-axes respectively, find its direction cosines.

2

Find the direction cosines of a line which makes equal angles with the coordinate axes.

3

If a line has the direction ratios –18, 12, –4, then what are its direction cosines?

4

Show that the points (2, 3, 4), (–1, –2, 1), (5, 8, 7) are collinear.

5

Find the direction cosines of the sides of the triangle whose vertices are (3, 5, –4), (-1, 1, 2) and (–5, –5, –2).