Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Three Dimensional Geometry

Short Answer Type

11. Find the direction ratios and the direction cosines of the lines joining the pairs of points:
(– 1, –1, –1), (2, 3, 4)

96 Views

12. Find the direction cosines of the line passing through the two points (–2, 4, –5) and (1, 2, 3).

191 Views

Long Answer Type

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

145 Views

Short Answer Type

14.

Find the direction cosines of the line joining the points (2, 1, 2) and (4, 2, 0).

93 Views

15.

A line makes angles of 45° and 60° with the positive axes of x and y respectively. What angle does it make with the positive axis of z?

481 Views

16. If α, β, γ are the angles which a line makes with the axes, prove that sin²α + sin² β + sin²γ = 2.

156 Views

17.
Show that the points (2, 3, 4), (–1, –2, 1), (5, 8, 7) are collinear.

Let P (2, 3, 4), Q (–1, –2, 1), R (5, 8, 7) be given points.
The direction ratios of PQ are –1, –2, –2 –3, 1 – 4 i.e. – 3, – 5, – 3
The direction ratios of PR are 5 – 2, 8 – 3, 7 –4 i.e. 3, 5, 3
Since

fraction numerator negative 3 over denominator 3 end fraction equals space fraction numerator negative 5 over denominator 5 end fraction equals fraction numerator negative 3 over denominator 3 end fraction

∴ lines PQ and PR are parallel.
But P is a common point on both the lines points
∴ P, Q, R are collinear.

119 Views

18. Show that the points (–1, 2, –3), (4, 5, 1) and (9, 8, 5) are collinear.

91 Views

19. Show that the points A(2, 3, – 4), B(1, –2, 3) and C (3, 8, –11) are collinear.

156 Views

20.

Find the length of the projection of the line segment joining the points P (3, -1, 2) and Q(2, 4, -1) on the line with direction ratios -1, 2, -2.

93 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

Long Answer Type

Short Answer Type

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

17.
Show that the points (2, 3, 4), (–1, –2, 1), (5, 8, 7) are collinear.