CBSE Class 12 Mathematics Vectors Algebra MCQs Set 02

Question. If a̅ is any vector, then

is equal to
(a) a̅
(b) 2a̅
(c) 3a̅
(d) 0

Answer : B

Question. A unit vector perpendicular to the plane ABC, where A, B and C are respectively the points (3, –1, 2), (1, –1, –3) and (4, –3, 1), is
(a) -1/√29 (2î + 5k̂)
(b) 1/√16(î – 2ĵ – k̂)
(c) 1/√26 (4î – 3ĵ +k̂)
(d) -1/√165 (10î + 7ĵ -4k̂)

Answer : D

Question.

(a) neither x nor y
(b) both x and y
(c) only x
(d) only y

Answer : A

Question. If the scalar product of the vector î+ ĵ+ k̂ vector along the sum of vectors 2î + 4ĵ – 5k̂ and λî + 2ĵ + 3k̂is equal to one then the value of λ is
(a) 0
(b) – 1
(c) 1/2
(d) 1

Answer : D

Question. Magnitude of the vector joining the points P(x₁, y₁, z₁) and Q(x₂, y₂, z₂) is
(a) (x₂ – x₁) + (y₂ – y₁) + (z₂ – z₁)
(b) (x₂ – y₂ + z₂) + (x₁ + y₁ + z₁
(c) √(x₂ – x₁)² + (y₂ – y1)²
(d) None of the above

Answer : D

Question. Which of the following represents graphically the displacement of 40 km, 30° East of North?

Answer : C

Question. Two vectors a̅ and b̅ are non-zero and non-collinear.
What is the value of x for which the vectors p̅ = ( x – 2) a̅ + b̅ and q̅ = (x + 1) a̅ – b̅ are collinear?
(a) 1
(b) 1/2
(c) 2/3
(d) 2

Answer : B

Question. If a̅ and b̅ are unit vectors inclined at an angle of 30° to each other, then which one of the following is correct ?

Answer : B

Question. Which of the following is/are true?
I. In a zero vector, initial and terminal points coincide.
II. Zero vector is denoted as O.
III. Zero vector has zero magnitude.
(a) Only II is true
(b) I and III are true
(c) II and III are true
(d) All are true

Answer : D

Question. The resultant moment of three forces î + 2ĵ – 3k̂ , 2î + 3ĵ + 4k̂ and -î – ĵ + k̂ acting on a particle at a point P (0, 1, 2) about the point A (1, –2, 0) is
(a) 6 √2
(b) √140
(c) √21
(d) None

Answer : B

Question. Which of the following is/are true?
I. To add two vectors a and b, they are positioned such that the initial point of one does not coincide with the terminal point of the other.
II. The resultant of the vectors AB and BC is represented by the third side AC of a triangle.
III. If sides of a triangle are taken in order, then it leads to zero resultant.
(a) Only I is true
(b) Only II is true
(c) II and III are true
(d) All are true

Answer : C

Question. If two vertices of a triangle are i – j and j + k, then the third vertex can be
(a) i + k
(b) i –2j – k and –2i – j
(c) i – k
(d) All the above

Answer : D

Question.

Answer : B

Question. If a̅ and b̅ are the two vectors such that a̅.b̅ = 0 and a̅ x b̅ = 0 , then
(a) a̅ is parallel to b̅ .
(b) a̅ is perpendicular to b̅ .
(c) either a̅ or b̅ is a null vector .
(d) None of these.

Answer : C

Question. The vector product of two non zero vector a and b, is denoted by a × b and is equal to
(a) |a| |b| cos θ
(b) a | | b sin θ n̅
(c) a | | b cos θ n̅
(d) None of these

Answer : B

Question. If | a̅ | = 5 , | b̅ | = 4 , | c̅ | = 3 , then the value of |a̅.b̅ + b̅.c̅ + c̅.a̅| , is equal to ( given that a̅ + b̅ + c̅ = 0 )
(a) 25
(b) 50
(c) –25
(d) –50

Answer : A

Question.

(a) 0
(b) 1
(c) – √3
(d) √3

Answer : A

Question. If |a̅| = 10 , |b̅| = 2 and a̅.b̅ = 12 , then the value of |a̅ x b̅| is
(a) 5
(b) 10
(c) 14
(d) 16

Answer : D

Question.

(a) 0
(b) 1
(c) 2
(d) 3

Answer : A

Question. If

are linearly dependent vectors and |c̅ | = √3 , then
(a) α = 1, β = – 1
(b) α = 1, β = ± 1
(c) α = – 1, β = ± 1
(d) α = β 1, ± = 1

Answer : D

Question. Which among the following figure correctly represents projection of AB on a line l ?

(d) All of these

Answer : D

Question. ABCDEF is a regular hexagon with centre at origin such that AD + EB + FC = λED, then λ is equal to
(a) 2
(b) 4
(c) 6
(d) 3

Answer : B

Question. The vector in the direction of the vector î – 2ĵ + 2k̂ that has magnitude 9 is
(a) î – 2ĵ + 2k̂
(b) î – 2ĵ + 2k̂/3
(c) 3(î – 2ĵ + 2k̂)
(d) 9(î – 2ĵ + 2k̂)

Answer : C

Question. In triangle ABC, which of the following is not true?

Answer : C

Question. If a̅ is a non-zero vector of magnitude a and l a non-zero scalar, then l a̅ is a unit vector if.
(a) l = 1
(b) l = – 1
(c) a = |l|
(d) a = 1/|λ|

Answer : D

Question. In the following table a̅ ≠ o̅ , b̅ ≠ o̅ and l1, m₁, n₁ and l₂, m₂, n₂ are their d.c. and a₁, b₁, c₁ and a₂, b₂, c₂ are their d. r.s respectively.

Codes
     A B C D E F
(a) 2 1 2 2 1 3
(b) 3 1 2 1 2 1
(c) 1 3 2 1 1 2
(d) 1 2 1 2 1 3

Answer : D

Question. For what value of m, are the points with position vector

(a) – 8
(b) 8
(c) 4
(d) – 4

Answer : B

Question. Let there be two points A, B on the curve y = x² in the plane OXY satisfying O̅A̅ . î = 1 and O̅B̅ . î = -2 , then the length of the vector 2O̅A̅ – 3O̅B̅ is
(a) 14
(b) 2 √51
(c) 3 √41
(d) 2 √41

Answer : D

Question. Consider the figure given below

Here, it is shown that a vector BC’ is having same magnitude as the vector BC, but its direction is opposite to that of it.
Based on above information which of the following is true?
(a) AC’ = a + b
(b) AC’ = a – b
(c) Difference of a and b is AC
(d) None of these

Answer : B

Assertion – Reason Type Questions :
(a) Assertion is correct, Reason is correct; Reason is a correct explanation for assertion.
(b) Assertion is correct, Reason is correct; Reason is not a correct explanation for Assertion
(c) Assertion is correct, Reason is incorrect
(d) Assertion is incorrect, Reason is correct.

Question. Consider the shown figure.

Assertion : If a and b represent the adjacent sides of a triangle as shown, then its area is 1/2|axb|
Reason : Area of ΔABC = 1/2|b||a| sin θ where, θ is the angle between the adjacent sides a and b (as shown).

Answer : A

Question. Assertion : In ΔABC , A̅B̅ + B̅C̅ + C̅A̅ = 0 .
Reason : If O̅A̅ = a̅, O̅B̅ = b̅ , then A̅B̅ = a̅+b̅ (triangle law of addition)

Answer : D

Question. Assertion : If I is the incentre of ΔABC , then |B̅C̅| I̅A̅ | C̅A̅ | I̅B̅ + |A̅B̅ | I̅C̅ = 0 .
Reason : The position vector of centroid of ΔABC is O̅A̅ + O̅B̅ + O̅C̅/3 .

Answer : C

Question. Assertion :

Reason : The projection of vector a on vector b is 1/|a| (a.b) .

Answer : C