Class XI Mathematics Quiz: Introduction to Three Dimensional Geometry
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Preview questions
1. What is the general form of the equation of a plane in three-dimensional geometry?
Ax + By + Cz + D = 0 · Ax + By + Cz = 0 · Ax^2 + By^2 + Cz^2 + D = 0 · A + B + C + D = 0
2. Which of the following represents the distance between a point and a plane?
|Ax_1 + By_1 + Cz_1 + D| / √(A^2 + B^2 + C^2) · √((x_1 - x_0)^2 + (y_1 - y_0)^2 + (z_1 - z_0)^2) · Ax_1 + By_1 + Cz_1 · D / (A + B + C)
3. What is the vector equation of a line in three-dimensional space?
r = a + tb · r = a + b + c · r = Ax + By + Cz · r = (x, y, z)
4. If two lines are skew, which of the following is true?
They are parallel. · They intersect at one point. · They lie in different planes. · They are coplanar.
5. What is the condition for two lines to be coplanar?
They must intersect. · The scalar triple product of their direction ratios is zero. · They must be parallel. · Their direction ratios must be equal.
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