Three Dimensional Geometry is crucial in CBSE and competitive exams because it builds the core ideas of lines, planes, and distances in 3D space. Concepts like skew lines, shortest distances, intersection lines, and perpendicularity directly appear in board exams and form high-weight questions in JEE/NEET, where students must handle vector and scalar triple-product based reasoning quickly and accurately.
15
Minutes
10
Questions
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Marking
Q1. A line passes through the point and has direction vector . A plane has equation . The shortest distance between and is
Q2. Two lines and are given by
The shortest distance between and equals
Q3. Let be the line of intersection of the planes
The perpendicular distance from the point to the line is
Q4. Find the plane passing through the line of intersection of the planes and which is perpendicular to the plane . The required plane is
Q5. Two skew lines are given by
Points on and on such that the segment is the shortest line joining the two lines are
on and on
on and on
on and on
on and on
Q6. Find the perpendicular distance of the point from the plane .
Q7. Find the shortest distance between the skew lines and .
Q8. Find the equation of the plane passing through the point and containing the line of intersection of the planes and .
Q9. The sphere meets the plane in a circle. The radius of that circle is
Q10. Let and be two planes. If is their line of intersection, a sphere centered at the origin tangent to has radius