MCQs For NCERT Class 12 Mathematics Chapter 10 Vector Algebra

Please refer to the MCQ Questions for Class 12 Mathematics Chapter 10 Vector Algebra with Answers. The following Vector Algebra Class 12 Mathematics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 12. Our experts have designed MCQ Questions for Class 12 Mathematics with Answers for all chapters in your NCERT Class 12 Mathematics book.

Vector Algebra Class 12 MCQ Questions with Answers

See below Vector Algebra Class 12 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

Question. The vector in the direction of the vector î – 2ĵ + 2k̂ that has magnitude 9 is

Question. Let a and b be two unit vectors and q is the angle between them. Then, a +b is a unit vector, if
(a) θ=π/4
(b) θ=π/3
(c) θ=π/2
(d)θ=2π/3

Question.

Question. If q is the angle between any two vectors a and b, then|a·b|=| axb| when θ is equal to 
(a) zero
(b) π/4
(c) θ=π/2
(d) θ=2π/3

Question. If the points (-1,-1,2), (2,m,5) ) and (3,11,6 ) are collinear, then the value of m is
(a) 2
(b) 4
(c) 6
(d) 8

Question. If θ is the angle between two vectors a and b, then a· b≥ 0 only when
(a) 0<θ<π/2
(b) 0≤ θ ≤ π/2
(c) 0 ≤ θ <π
(d) 0 ≤ θ ≤ π

Question. A vector r of magnitude 3√2 units which makes an angle of π/4 and π/2 with y and z-axes, respectively is

Question. If| a| =8|b|= 3 and|axb| = 12, then value ofa· b× is
(a) 6√3
(b) 8√3
(c) 12√3
(d) None of these

Question. The projection of vector

(a) 2/3
(b) 1/3
(c) 2
(d) 6

Question.

is
(a) -1
(b) -2
(c) 1
(d) 2

Question. The two vectors 

represents the two sides AB and AC, respectively of a ΔABC. The length of the median through A is 
(a) √34/2
(b) √48/2
(c) √18
(d) None of these

Question. The unit vector perpendicular to the vectors 

and

forming a right handed system is

Question. If|a|a= 3 and -1≤k ≤ 2,then| ka|lies in the interval
(a) [ 0, 6]
(b) [-3, 6] 
(c) [3, 6]
(d) [1, 2]

Question. If a and b are unit vectors, then what is the angle between a and b for 3 a b – to be a unit vector ?
(a) 30°
(b) 45°
(c) 60°
(d) 90°

Question. If a and b are the position vectors of A and B ,respectively, then the position vector of a point C in BA produced such that BC= BA = 1.5 BA is
(a) 3a- b
(b) a -b3b
(c) 0.5(a-3b)
(d) 0.5(3a-b)

Question. The sine of the angle between the vectors

Question. Find the value of l such that the vectors

(a) 0
(b) 1
(c) 3/2
(d) -5/2

Question. If A, B, C and D are the points with position vectors//38 respectively, Then, the projection of AB along CD is
(a) 1/√21
(b) √21
(c) √3/7
(d) 2/√21

Question.

Question. The position vector of the point which divides the join of points 2 a̅ – 3 b̅ – and a̅ + b̅ in the ratio 3 : 1, is

Question. The vector having initial and terminal points as (2, 5, 0) and (-3, 7,4), respectively is
(a) – î + 12ĵ + 4k̂
(b) 5î + 2ĵ – 4k̂
(c) -5î + 2ĵ + 4k̂
(d) î + ĵ + k̂

Question. The angle between two vectors a̅ and b̅ with magnitudes √3 and 4, respectively and a̅ · b̅ × = 2√3 is
(a) π/6
(b) π/3
(c) π/2
(d) 5π/2

Question. Find the value of λ such that the vectors a = 2î + λĵ + k̂ and b = 2î + 2ĵ + 3k̂ are orthogonal.
(a) 0
(b) 1
(c) 3/2
(d) -5/2

Question. The value of λ for which the vectors 3î + 6ĵ + k̂ and 2î – 4ĵ + λk̂ are parallel, is
(a) 2/3
(b) 3/2
(c) 5/2
(d) 2/5

Question. The vectors from origin to the points A and B are = 2î – 3ĵ + 2k̂ and 2î – 3ĵ + k̂ respectively, then the area of ΔOAB is equal to

Question.

Question.

(a) 5
(b) 10
(c) 14
(d) 16

Question. The vectors λî + ĵ + 2k̂, î + λĵ – k̂ and 2î + ĵ + λk̂are coplanar, if
(a) λ = -2
(b) λ = 0
(c) λ =1
(d) λ = -1

Question.

(a) 1
(b) 3
(c) – (3/2)
(d) None of these

Question. The projection vector of a̅ on b̅ is

Question.

(a) 0
(b) 1
(c) -19
(d) 38

Question. If |a̅| = 4 and -3 < λ < 2 , then the range of |λa̅| is
(a) [0, 8]
(b) [-12, 8]
(c) [0, 12]
(d) [8, 12]

Question. The number of vectors of unit length perpendicular to the vectors a̅ = 2î + 2ĵ + 2k̂ and b̅ = ĵ + k̂ is
(a) one
(b) two
(c) three
(d) infinite

True/False

Question. If |a̅| = |b̅| , then necessarily it implies a̅ = ± b̅

Question. Position vector of a point p̅ is a vector whose initial point is origin.

Question. If | a̅ + b̅| = | a̅ – b̅|, then the vectors a̅ and b̅ are orthogonal

Question.

Question. If a̅ and b̅ are adjacent sides of a rhombus, then a̅ · b̅ = 0

The vertices of a Δ ABC are A(2,0,2), B=(-1, 1, 1) 4 T and C=(1,-2,4). The points D and E divide the sides A, B and C A in the ratio 1 :2 , respectively. Another point F is taken in space such that perpendicular drawn from F on ΔABC,meets the triangle at the point of intersection of the line segment CD and BE, say P. If the distance of F from the plane of the Δ ABC is √2 units, then On the basis of the above information, answer the following question.

Question. The position vector of P is

Question. The volume of the tetrahedron ABCF is
(a) 7 cu units
(b) 3/5 cu units
(c) 7/3 cu units
(d) 7/5 cu units

Each of these questions contains two statements : Statement I (Assertion) and Statement II (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.
(a) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
(b) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
(c) Statement I is true; Statement II is false.
(d) Statement I is false; Statement II is true.

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