Three Dimensional Geometry: Class 12 Mathematics (UP Board) important questions and practice
Three Dimensional Geometry is chapter 11 of 13 in UP Board Class 12 Mathematics. Below are the topics the paper draws from, the question types that come up again and again, and a free practice test on this chapter alone.
Topics in this chapter
- Direction cosines and direction ratios of a line
- Equation of a line in vector and Cartesian form
- Angle between two lines
- Shortest distance between two skew lines and distance between parallel lines
- Coplanarity and intersection of lines
What examiners usually ask
- Find the shortest distance between the lines r = (i + 2j + k) + t(i - j + k) and r = (2i - j - k) + s(2i + j + 2k)
- Find the vector and Cartesian equations of the line passing through (1, 2, 3) and parallel to the line (x - 2)/3 = (y + 1)/-2 = z/4
- Find the angle between the lines with direction ratios 1, 2, 2 and 2, 1, -2
Exam tip
The shortest distance formula between skew lines is a near-certain 3-5 mark question; write b1 x b2 as a determinant, compute |(a2 - a1) . (b1 x b2)| and divide by |b1 x b2|, and note that the plane topics are removed from the rationalised CBSE syllabus.
Three Dimensional Geometry on other boards and exams
Frequently asked questions
What are the important questions from Three Dimensional Geometry for UP Board Class 12?
The question types listed above repeat most often in UP Board Class 12 Mathematics papers for this chapter. Practise them with the chapter test and then attempt them inside a full previous-year paper under time.
Is Three Dimensional Geometry in the UP Board Class 12 Mathematics syllabus?
Yes. Three Dimensional Geometry is part of the current UP Board Class 12 Mathematics syllabus, as listed on this site from the prescribed textbook.
Can I practise Three Dimensional Geometry MCQs in Hindi?
Yes. The chapter test and explanations are available in Hindi and English, with an AI doubt solver for any question.