Vector Algebra

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

Difficulty: 37 easy · 108 moderate · 13 hard.
Most-asked subtopics: Scalar (Dot) Product and Projection (62), Vector (Cross) Product (39), Addition of Vectors (20).
Updated 19 August 2026.

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#1Types of Vectors
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.
#2Types of Vectors
#3Types of Vectors
An instructor at the astronomical centre shows three among the brightest stars in a particular constellation. Assume that the telescope is located at O(0, 0, 0) and the three stars have their locations at the points D, A and V having position vectors $2\hat{i} + 3\hat{j} + 4\hat{k}$ , $7\hat{i} + 5\hat{j} + 8\hat{k}$ and $-3\hat{i} + 7\hat{j} + 11\hat{k}$ respectively. Based on the above information, answer the following questions :
#4Types of Vectors
#5Types of Vectors
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#6Types of Vectors
#7Types of Vectors
#8Types of Vectors
#9Types of Vectors
#10Types of Vectors
#11Addition of Vectors
#12Addition of Vectors
#13Addition of Vectors
#14Addition of Vectors
#15Addition of Vectors
#16Addition of Vectors
#17Addition of Vectors
#18Addition of Vectors
#19Addition of Vectors
#20Addition of Vectors
Direction : In questions numbers 19 and 20, two statements are given one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the following options :
#21Addition of Vectors
#22Addition of Vectors
An instructor at the astronomical centre shows three among the brightest stars in a particular constellation. Assume that the telescope is located at O(0, 0, 0) and the three stars have their locations at the points D, A and V having position vectors $2\hat{i} + 3\hat{j} + 4\hat{k}$ , $7\hat{i} + 5\hat{j} + 8\hat{k}$ and $-3\hat{i} + 7\hat{j} + 11\hat{k}$ respectively. Based on the above information, answer the following questions :
#23Addition of Vectors
#24Addition of Vectors
#25Addition of Vectors
#26Addition of Vectors
#27Addition of Vectors
#28Addition of Vectors
Three friends A, B and C move out from the same location O at the same time in three different directions to reach their destinations. They move out on straight paths and decide that A and B after reaching their destinations will meet up with C at his predecided destination, following straight paths from A to C and B to C in such a way that $\overrightarrow{OA} = \vec{a}$ , $\overrightarrow{OB} = \vec{b}$ and $\overrightarrow{OC} = 5\vec{a} - 2\vec{b}$ respectively. Based upon the above information, answer the following questions :
#29Addition of Vectors
Three friends A, B and C move out from the same location O at the same time in three different directions to reach their destinations. They move out on straight paths and decide that A and B after reaching their destinations will meet up with C at his predecided destination, following straight paths from A to C and B to C in such a way that $\overrightarrow{OA} = \vec{a}$ , $\overrightarrow{OB} = \vec{b}$ and $\overrightarrow{OC} = 5\vec{a} - 2\vec{b}$ respectively. Based upon the above information, answer the following questions :
#30Addition of Vectors
#31Components and Direction Cosines
#32Components and Direction Cosines
#33Components and Direction Cosines
#34Components and Direction Cosines
#35Components and Direction Cosines
#36Components and Direction Cosines
#37Components and Direction Cosines
#38Components and Direction Cosines
#39Components and Direction Cosines
#40Components and Direction Cosines
#41Components and Direction Cosines
#42Components and Direction Cosines
#43Components and Direction Cosines
#44Components and Direction Cosines
#45Section Formula
#46Section Formula
#47Section Formula
#48Section Formula
#49Section Formula
#50Section Formula

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