Worksheets Class 12 Mathematics Vector Algebra

Students should refer to Worksheets Class 12 Mathematics Vector Algebra Chapter 10 provided below with important questions and answers. These important questions with solutions for Chapter 10 Vector Algebra have been prepared by expert teachers for Class 12 Mathematics based on the expected pattern of questions in the class 12 exams. We have provided Worksheets for Class 12 Mathematics for all chapters on our website. You should carefully learn all the important examinations questions provided below as they will help you to get better marks in your class tests and exams.

Vector Algebra Worksheets Class 12 Mathematics

Question. If DA a AB b = = , and CB a =k , wherek > 0and X Y, are the mid-points of DB and AC respectively such that |a|  =17 and | XY | =4, then k is
equal to
(a) 8/17
(b) 9/17
(c) 5/17
(d) 4/17

Question. If a and b are two unit vectors inclined to x-axis at angles 30° and 120°, then| | a b + is equal to

(a)√2/3
(b)√2
(c)√3
(d)2

Question. 

Question. What is the value of (d+a )· [ax {bx (cxd)}] ?
(a) (d· a) ·[b c d]
(b) (a· d) ·[b c d]
(c) (b· d) ·[a c d]
(d) (b· d) ·[a d c] 

Question.

Question.

Question. 

Question.

Question. 
(a) 60
(b) 68
(c) -60
(d) -74

Question.

Question.

(a) c₁ = 0
(b) c₁ = 1
(c) c₁ = 2
(d) no value of c₁ can be found

Question. The sum of two unit vectors is a unit vector. The magnitude of their difference is
(a) 2
(b) √3
(c) √2
(d) 1

Question. For non-zero vector a and b, if |a+b|< |a-b|, then a and b are  
(a) collinear
(b) perpendicular to each other
(c) inclined at an acute angle
(d) inclined at an obtuse angle

Question. (ax b)x= ax(b x c) if
(a) (a x b)x c =0 
(b) c x a=b 
(c) (a x c) x b =0
(d) a·(b x c)

Question. The angle between and b is π/6, then angle between 2a and 3b is
(a) π/3
(b) π/2
(c) π/6
(d) 3π/4

Question. If a and b are two unit vectors such that a b + 2 and 5a- 4b – are perpendicular to each other, then the angle between a and b is
(a) 30°
(b) 60°
(c) cos- 1(3/5)
(d) cos- 1(4/7)

Question. 

Question.

(a) √14
(b) 2√51
(c) 3√41
(d) 2√41

Question.

(a) π/6
(b) 2π/3
(c) π/3
(d) 5π/3

Question.

(a) 30°
(b) 45°
(c) 60°
(d) 15° 

Question.

Question. If a and b are unit vectors, then the greatest value of
|a+b |+ |a-b| is
(a) 2
(b) 4
(c) 2√2
(d) √2

Question. If a, b and c are non-coplanar vectors and r is a real number, then the vectors a+2b +3c, λb+4c  and
(2λ- 1)c are non-coplanar for
(a) no value ofλ
(b) all except one value of λ
(c) all except two values of λ
(d) all values ofλ

Question. Let u v, and w be three vectors such that |u | =1|v |=2,|w| = 3. If the projection of v along u is equal to that of w along u , v and w are perpendicular to each other, then |u-v+w| is equal to
(a) 4
(b) √7
(c) √14
(d) 2

Question. If V is the volume of the parallelopiped having three coterminus edges, as a, b and c, then the volume of the parallelopiped having three coterminus edges as

Question.

Question.

(a) 1
(b) 2
(c) 3
(d) 4

Question. Vectors a and b are such that |a|=1,| b|=4 and a · b× = 2. If c =2axb- 3b , then the angle between b and c is
(a) π/6
(b) 5/π
(c) π/3
(d) 2π/3

Question. 

(a) 10
(b) 8
(c) 2√26
(d) 6

Question.

Question. Let ABCD be a parallelogram whose diagonals intersect at P and let O be the origin, then OA+ OB+ OC+ OD  equal to
(a) OP
(b) 2OP
(c) 3OP
(d) 4OP

Question. The position vectors of three points are 2a-b+3c,a-2b+λc and µa-5b, where a ,b and c are non-coplanar vectors. The points are collinear, when

Question. If ABCD is a rhombus whose diagonals cut at the origin O, then OA+ OB+ OC+ OD equals
(a) AB+ AC 
(b) O
(c) 2(AB +BC)
(d) AC+ BD 

Question. A point O is the centre of circle circumscribed about a ΔABC. Then,OA sin2A+0B sin2B+0C sin 2C is equal to
(a) ( OA+OB+OC))sin 2A
(b) 3OG, where Gis centroid of ΔABC
(c) O
(d) None of the above 

Question. If a and bare position vectors of A and B respectively and C is a point on AB produced such that AC= 3AB   then position vector of C is
(a) 3a -2b 
(b) 3b- 2a
(c) 3b+ 2a
(d) 2a-3b

Question. ABCD is a parallelogram, A₁ and B₁are mid-points of side BC and CD respectively. If AA₁+ BB₁ = λAC then λ is equal to
(a) 1/2
(b) 1
(c) 3/2
(d) 2   

CHAK 2
Question. If θ be the angle between the unit vectors a and b, then cos θ/2 is equal to

Question.

Question. If the scalar projection of the vector

on the vector

then the value of x is equal to
(a) – 5 /2
(b) 6
(c) -6
(d) 3 

Question.

Question. If|a |b |c| and a+ b= c,  then the angle between a and b is
(a) π /2
(b) p
(c) 0
(d) None of these 

Question. The area of the parallelogram whose diagonals are

 and

(a) 4 √3
(b) 5 √3
(c) 8
(d) 4 

Question.

(a) 3
(b) 4
(c) 5
(d) 6 

Question. If the vectors 2i+j+ k and i-4j+λ k are perpendicular, then λ is  equal to
(a) 4
(b) -5
(c) 2
(d) 1

Question.

Question. If θ is the angle between the vectors a and band| axb|= |a,b| then θ is
(a) 0
(b) 180°
(c) 135°
(d) 45°

Question. The angle between two vectors a and b with magnitudes √3 and 2 respectively, having a ·b = √6 is 
(a) √/4
(b) π/2
(c) π/6
(d) π/3

Question. If a and b are two collinear vectors, then which of the following are incorrect? 
(a) b = λa, for some scalar λ
(b

(c) The respective components of a and b are proportional.
(d) Both the vectors a and b have same direction but different magnitudes.

Question.

(a) 60/√122
(b) 30/√144
(c) 60/√144
(d) 60/√111

Question.

Question. If for a unit vector a, (x -a)· (x+a) = 12, then|x| is equal to
(a) 4
(b) 2
(c) 13
(d) 11

Question. The magnitude of two vectors a and b having the same magnitude and such that the angle between them is 60° and their scalar product is 1/2 are

Question.

is
(a) 2
(b) 4
(c) 6
(d) 8

Question. For any two non-zero vectors a and b, |a |b+| b| a and |a| b-| b| a are 
(a) parallel
(b) perpendicular
(c) non-parallel
(d) None of these

Question. If a, b c, are unit vectors such that a +b+ c = 0,then the value of a· b +b · c +c· a  is 
(a) 0
(b) -1/2
(c) -3/2
(d) 2/11.

Question. If the vertices A, B, C of a ΔABC have position vectors (1,2,3), (-1,0,0),(0,1,2)  respectively, then ∠ABC (∠ABC is the angle between the vectors BA and BC), is equal to 
(a)π/2
(b) π/4
(c) cos^-1(10/√102)
(d) cos^-1(1/3)

Question. If a· a× = 0 and a· b = 0, then what can be conclude about the vector b? 
(a) Any vector
(b) Zero-vector
(c) Unit vector
(d) None of these 

Question. Given that a· b = 0 and ax b = 0. What can you conclude about the vectors a and b? 
(a) a and b can be perpendicular and parallel simultaneously
(b) |a| = 0 or |b| = 0
(c) |a| = 0 and |b| = 0
(d) None of the above

Question. A unit vector in XY-plane, making an angle of 30° in anti-clockwise direction with the positive direction of X-axis is

Question. The points A(1,2,7), B( 2,6,3) and C( 3,10,-1) are
(a) collinear
(b) coplanar
(c) non-collinear
(d) None of these 

Question. If a = b+ c, then which of the following statements is correct? 
(a) | a| =|= |c| 
(b) | a|+|b| =|c| 
(c) | a|b| +|c|
(d) None of these

Question. A vector of magnitude 5 units and parallel to

Question. Find the position vector of point R which divides the line joining two points p(2a+b) and Q(a-3b) externally in the ratio 1:2 . Also, show that P is the middle point of the line segment RQ. 
(a) 2a + b
(b) 5a+ 3b 
(c) 3a+ 5b
(d) None of these

Question. The value of x for which

is a unit vector
a) ± 1/ √3
(b) ± 1√3
(c) ± 1/2
(d) ± 1/√2

Question.

Question.

(a) 1
(b) 2
(c) 3
(d) 4

Question. The two adjacent sides of a parallelogram are