# Three Dimensional Geometry

This is an MCQ-based quiz on Three Dimensional Geometry.

This includes Direction cosines, Direction Ratios, Equation of Line, Angle between two lines, and Shortest Distance

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The direction cosines of the y-axis are

(6, 0, 0) (1, 0, 0) (0, 1, 0) (0, 0, 1)

The coordinates of the midpoints of the line segment joining the points (2, 3, 4) and (8, -3, 8) are

(10, 0, 12) (5, 6, 0) (6, 5, 0) (5, 0, 6)

The distance of the plane 2x – 3y + 6z + 7 = 0 from the point (2, -3, -1) is

4 3 2 1/5

If 2x + 5y – 6z + 3 = 0 be the equation of the plane, then the equation of any plane parallel to the given plane is

3x + 5y – 6z + 3 = 0 2x – 5y – 6z + 3 = 0 2x + 5y – 6z + k = 0 None of these

The length of the ⊥er from the point (0, – 1, 3) to the plane 2x + y – 2z + 1 = 0 is

0 2√3 2/3 2

If α, ß, γ are the angles that a line makes with the positive direction of x, y, z axis, respectively, then the direction-cosines of the line are:

< sin α, sin ß, sin γ > < cos α, cos ß, cos γ > < tan α, tan ß, tan γ > < cos² α, cos² ß, cos² γ >.

What is the distance (in units) between two planes: 3x + 5y + 7z = 3 and 9x + 15y + 21z = 9?

0 3 6 / sqrt(83) 6.

The co-ordinates of the foot of the perpendicular drawn from the point (2, 5, 7) on the x-axis are given by:

(2, 0, 0) (0, 5, 0) (0, 0, 7) (0, 5, 7).

The reflection of the point (α, ß, γ) in the xy-plane is:

(α, ß, 0) (0, 0, γ) (-α, -ß, γ) (α, ß, -γ).

The planes 2x – y + 4z = 3 and 5x – 2.5y +10 z = 6 are

Perpendicular

Parallel

Intersect along y-axis

Passes through (0, 0, 5/4)

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

1 2 0 -1

If a line makes angles α, β, γ with the axis then cos 2α + cos 2β + cos 2γ =

-2 -1 1 2

The equation of the plane through point (1, 2, -3) which is parallel to the plane 3x- 5y + 2z = 11 is given by

3x – 5y + 2z – 13 = 0 5x – 3y + 2z + 13 = 0 3x – 2y + 5z + 13 = 0 3x – 5y + 2z + 13 = 0

The area of the quadrilateral ABCD, where A(0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2, 6, 2) is equal to

9 sq. units 18 sq. units 27 sq. units 81 sq. units

The line x = 1, y = 2 is

Parallel to x-axis

Parallel to y-axis

Parallel to z-axis

None of these

Quiz/Test Summary
Title: Three Dimensional Geometry
Questions: 15
Contributed by: 