Basic Math XII- 3D Coordinates

The point (4, 0, 0) lies on _

• X-axis

• Y-axis

• Z-axis

• Y-Z plane

The point (0, 2, 4) lies on _

• X-Y plane

• Y-Z plane

• X-Z plane

• X-axis

Find the distance of point (2, 3, 5) from X-Y plane.

• 2 units

• 3 units

• 5 units

• 1 unit

In which octant does the point (-1, – 5, -7) lie?

• First

• Second

• Sixth

• Seventh

What is the distance between two points (5, 6, 7) and (2, 6, 3)?

• 3 units

• 0 units

• 4 units

• 5 units

Are A (3, 2, 1), B (5, 3, -2) and C (-1, 0, 7) collinear points?

• Yes

• No

In which ratio (3, 4, 5) divides the line segment joining (1, 2, 3) and (4, 5, 6) internally?

• 1:2

• 2:1

• 3:4

• 4:3

In which ratio does the line joining (1, 2, 3) and (4, 5, 6) divide X-Y plane?

• -2:1

• 1:2

• -1:2

• 2:1

The reflection of the point (α, β, γ) in the XY-plane is....

• (α, β, 0)

• (0, 0, γ)

• (-α, -β, -γ)

• (α, β, -γ)

Direction cosines of the line that makes equal angles with the three axes in space are ...

• $\pm\frac{1}{\sqrt{3}},\pm\frac{1}{3},\pm\frac{1}{3}$

• $\pm\frac{6}{7},\pm\frac{2}{7},\pm\frac{3}{7}$

• $\pm\frac{1}{\sqrt{3}},\pm\frac{1}{\sqrt{3}},\pm\frac{1}{\sqrt{3}}$

• $\sqrt{\frac{1}{7}},\pm\sqrt{\frac{3}{14}},\frac{1}{\sqrt{14}}$