Three Dimensional Geometry Quiz
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Preview questions
1. What is the general equation of a plane in three-dimensional geometry?
Ax + By + Cz + D = 0 · Ax + By + C = 0 · Ax^2 + By^2 + Cz^2 = 0 · A + B + C = 0
2. The distance between the point (x1, y1, z1) and the point (x2, y2, z2) in 3D is given by which formula?
√((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2) · √((x2+x1)^2 + (y2+y1)^2 + (z2+z1)^2) · √((x2-x1)^2 + (y2+y1)^2 + (z2+y1)^2) · √((x1-x2)^2 + (y1-y2)^2 + (z1-z2)^2)
3. What is the angle between two vectors A and B given by A·B = |A||B|cosθ?
θ = cos^(-1)(A·B / |A||B|) · θ = sin^(-1)(A·B / |A||B|) · θ = tan^(-1)(A·B / |A||B|) · θ = A·B + |A||B|
4. What is the direction cosines of a line making angles α, β, and γ with the coordinate axes?
l = cosα, m = cosβ, n = cosγ · l = sinα, m = sinβ, n = sinγ · l = tanα, m = tanβ, n = tanγ · l = α, m = β, n = γ
5. The equation of a line in space can be represented in which form?
r = a + tb · r = a - tb · r = at + b · r = a/b
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