Three Dimensional Geometry

153 CBSE Class 12 Mathematics past-year questions from 5 papers, 2022 to 2026, with answers and worked solutions.

Difficulty: 24 easy · 78 moderate · 51 hard.
Most-asked subtopics: Equation of a Line in Space (69), Direction Cosines and Direction Ratios (31), Shortest Distance Between Two Lines (24).
Updated 19 August 2026.

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#1Direction Cosines and Direction Ratios
#2Direction Cosines and Direction Ratios
#3Direction Cosines and Direction Ratios
#4Direction Cosines and Direction Ratios
#5Direction Cosines and Direction Ratios
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#6Direction Cosines and Direction Ratios
#7Direction Cosines and Direction Ratios
#8Direction Cosines and Direction Ratios
#9Direction Cosines and Direction Ratios
#10Direction Cosines and Direction Ratios
Direction : Question numbers 19 and 20 are Assertion (A) and Reason (R) based questions carrying 1 mark each. Two statements are given, one labelled Assertion (A) and other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.
#11Direction Cosines and Direction Ratios
#12Direction Cosines and Direction Ratios
#13Direction Cosines and Direction Ratios
#14Direction Cosines and Direction Ratios
#15Direction Cosines and Direction Ratios
#16Direction Cosines and Direction Ratios
#17Direction Cosines and Direction Ratios
#18Direction Cosines and Direction Ratios
Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.
#19Direction Cosines and Direction Ratios
#20Direction Cosines and Direction Ratios
#21Direction Cosines and Direction Ratios
#22Direction Cosines and Direction Ratios
#23Direction Cosines and Direction Ratios
#24Direction Cosines and Direction Ratios
#25Direction Cosines and Direction Ratios
#26Direction Cosines and Direction Ratios
#27Direction Cosines and Direction Ratios
In the following questions 19 & 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct answer out of the following choices :
#28Direction Cosines and Direction Ratios
#29Direction Cosines and Direction Ratios
#30Direction Cosines and Direction Ratios
#31Direction Cosines and Direction Ratios
#32Equation of a Line in Space
#33Equation of a Line in Space
#34Equation of a Line in Space
#35Equation of a Line in Space
Two motorcycles A and B are running at the speed more than the allowed speed on the roads represented by the lines $\vec{r} = \lambda\left(\hat{i} + 2\hat{j} - \hat{k}\right)$ and $\vec{r} = \left(3\hat{i} + 3\hat{j}\right) + \mu\left(2\hat{i} + \hat{j} + \hat{k}\right)$ respectively. Based on the above information, answer the following questions :
#36Equation of a Line in Space
#37Equation of a Line in Space
Electrical transmission wires which are laid down in winters are stretched tightly to accommodate expansion in summers. Two such wires lie along the following lines : $l_1 : \frac{x + 1}{3} = \frac{y - 3}{-2} = \frac{z + 2}{-1}$ $l_2 : \frac{x}{-1} = \frac{y - 7}{3} = \frac{z + 7}{-2}$ Based on the given information, answer the following questions :
#38Equation of a Line in Space
#39Equation of a Line in Space
#40Equation of a Line in Space
#41Equation of a Line in Space
#42Equation of a Line in Space
#43Equation of a Line in Space
#44Equation of a Line in Space
#45Equation of a Line in Space
#46Equation of a Line in Space
#47Equation of a Line in Space
#48Equation of a Line in Space
#49Equation of a Line in Space
#50Equation of a Line in Space

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Three Dimensional Geometry

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