Vectors: Class 12 Previous Year Questions

Vectors questions asked in CBSE board exams

Repeated questions first. Open the free app to see each question as it appeared in the paper, with its marking scheme.

1. The equation of a line parallel to the vector 3i + + 2k and passing 9. through the point (4, -3, 7) is : (A) x= 4t + 3, y =-3t + 1, z= 7t + 2 (B) x=3t+4,y=t+3,z=2t+7 (C) x= 3t + 4, y = t - 3, z = 2t + 7 (D) x = 3t + 4, y =-t + 3, z = 2t + 7 Page 7 of 24 10. ,,…
   Board 20251 markMCQRepeated: 2023,2025
2. If a, , are three non-zero unequal vectors such that a. = a. , then find the angle between a and - . 1
   Board 20232 marksshort answerRepeated: 2022,2023
3. Page 3 of 7 3. a and b are two unit vectors such that |2a + 3 b | = | 3a 2 b |. Find the angle between a and b .
   Board 20221 markvery shortRepeated: 2022,2023
4. { } 35. A line passing through the points A(1, 2, 3) and B(5, 8, 11) intersects the line r = 4^i + ^j + (5^i + 2^j + ^k ). Find the co-ordinates of the point of intersection. Hence, write the equation of a line passing through the point of intersection and p…
   Board 20265 markslong answer
5. Find the vector of magnitude 14 in the direction of  QP, where P and Q are the points (1, 3, 2) and (–1, 0, 8) respectively. 2     
   Board 20262 marksshort answer
6. The value of m for which the points with position vectors –  i –  j + 2  k, 2  i + m  j + 5  k and 3  i + 11  j + 6  k are collinear, is 1 (A) 8 (B) –8 (C) 2 (D) 5
   Board 20261 markMCQ
7. The value of p for which vectors  i + 2  j + 3  k and 2  i – p  j +  k are perpendicular to each other is 1 (A) 0 (B) 1 (C) 5 2 (D) – 5 2   
   Board 20261 markMCQ
8. Vectors a = 3  i – 2  j + 2  k and b =  i + 2  k represent the two adjacent sides of a parallelogram. Find the vectors representing its diagonals and hence find their lengths. 2   x x 2 sin 2 cos 
   Board 20262 marksshort answer
9. Vector of magnitude 3 making equal angles with x and y axes and perpendicular to z axis is 1 (A) ^i + 2 2 ^j (B) 3^k (C) 2 2 3 ^i + 2 2 3 ^j (D) 3 ^i + 3 ^j + 3 ^k 1 1
   Board 20261 markMCQ
10. If  – AB = ^j + ^k and  – AC = 3^i –^j + 4^k represent the two vectors along the sides AB and AC of ABC, prove that the median 2 – AC – AB – AD      , where D is midpoint of BC. Hence, find the length of median AD. 2  ^ ^ ^ ^ ^
    Board 20262 marksshort answer
11. If a and b are two non-collinear vectors, then find x, such that & = (x - 2) a + b and · = (3 + 2x) a - 2b are collinear. dy
    Board 20252 marksshort answer
12. If vector a = 3i + 2 - and vector =i - + k, then which of the 2. following is correct ? (A) (B) (C) (D)
    Board 20251 markMCQ
13. Let and be two unit vectors and · be the angle between them. Then an o oa n q I ( + ) (A) (B) 2· (C) (D)
    Board 20251 markMCQ
14. l. (a) A vector a makes equal angles with all the three axes. If the magnitude of the vector is 53 units, then find a. OR (b) If · and · are position vectors of two points P and Q respectively, then find the position vector of a point R in QP produced such tha…
    Board 20252 marksshort answer
15. (a) Two friends while flying kites from different locations, find the strings of their kites crossing each other. The strings can be represented by vectors a = 3i + + 2k and = 2i - 2§ + 4k. Determine the angle formed between the kite strings. Assume there is n…
    Board 20252 marksshort answer
16. If ® a and ® b are two non-zero vectors such that ( ® a + ® b ) z ® a and (2 ® a + ® b ) z ® b , then prove that | ® b | = 2 | ® a |. ® ^ ^ ^
    Board 20242 marksshort answer
17. Page 8 of 23 16. aoIm 2 1 – x = – y = 6 1 z 2 + Ho$ g_m§Va EH$ g{Xe Ho$ {XH$²-AZwnmV h¢ : (A) 2, – 1, 6 (B) 2, 1, 6 (C) 2, 1, 3 (D) 2, – 1, 3 666 Page 9 of 23 11. Let E be an event of a sample space S of an experiment, then P(S|E) = (A) P(S 3 E) (B) P(E) (C) 1…
    Board 20241 markMCQ
18. (a) Find the equations of the diagonals of the parallelogram PQRS () ())() Use these equations to find the point of intersection of diagonals. OR (b) A line l passes through point (-1, 3, -2) and is perpendicular to both y-1 z+ 1 Find the vector equation of th…
    Board 20235 markslong answer
19. Position vector of the mid-point of line segment AB is 3i + 2j - 3k. If position vector of the point A is 2i + 3j - 4k, then position vector of the point Bis 4i+-2k (A) (B) (C) 5i + 5 - 7k (D)
    Board 20231 markMCQ
20. Find all the vectors of magnitude 3 3 which are collinear to vector ^i + ^j + ^k .
    Board 20232 marksshort answer

Practise all 41 Vectors questions with answers →

Other Class 12 Maths chapters

Frequently asked questions