CBSE Class 12 Maths Three Dimensional Geometry Quiz 2

1. The equation x² – x – 2 = 0 in three dimensional space is represented by

A A pair of parallel planes B A pair of straight lines C A pair of perpendicular plane D None of these

2. The distance of the point (-3, 4, 5) from the origin

A 50 B 5√2 C 6 D None of these

3. The direction ratios of a line are 1,3,5 then its direction cosines are

A \(\frac{1}{\sqrt{35}}\), \(\frac{3}{\sqrt{35}}\), \(\frac{5}{\sqrt{35}}\) B \(\frac{1}{9}\), \(\frac{1}{3}\), \(\frac{5}{9}\) C \(\frac{5}{\sqrt{35}}\), \(\frac{3}{\sqrt{35}}\), \(\frac{1}{\sqrt{35}}\) D None of these

4. The direction ratios of the normal to the plane 7x + 4y – 2z + 5 = 0 are

A 7, 4,-2

5. The direction ratios of the line of intersection of the planes 3x + 2y – z = 5 and x – y + 2z = 3 are

A 3, 2, -1 B -3, 7, 5 C 1, -1, 2 D – 11, 4, -5

6. The lines of intersection of the planes \(\vec{r}\)(3\(\hat{i}\) – \(\hat{j}\) + \(\hat{k}\)) = 1 and \(\vec{r}\)(\(\hat{i}\) +4\(\hat{j}\) – 2\(\hat{k}\)) = 2 is parallel to the vector

A 2\(\hat{i}\) + 7\(\hat{j}\) + 13\(\hat{k}\) B -2\(\hat{i}\) – 7\(\hat{j}\) – 13\(\hat{k}\) C 2\(\hat{i}\) – 7\(\hat{j}\) + 13\(\hat{i}\)

7. The equation of the plane through the origin and parallel to the plane 3x – 4y + 5z + 6 = 0

A 3x – 4y – 5z – 6 = 0 B 3x – 4y + 5z + 6 = 0 C 3x – 4y + 5z = 0 D 3x + 4y – 5z + 6 = 0

8. The locus of xy + yz = 0 is

A A pair of st. lines B A pair of parallel lines C A pair of parallel planes D A pair of perpendicular planes

9. The plane x + y = 0

A is parallel to z-axis B is perpendicular to z-axis C passes through z-axis D None of these

10. If α, β, γ are the angle which a half ray makes with the positive directions of the axis then sin²α + sin²β + sin²γ =

A 1 B 2 C 0 D -1