NCERT MCQ CLASS-12 CHAPTER-10 | MATH NCERT MCQ | VECTOR ALGEBRA | EDUGROWN

In This Post we are  providing Chapter-10 Vector Algebra NCERT MCQ for Class 12 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON VECTOR ALGEBRA

Question 1.
In ΔABC, which of the following is not true?

(a) AB→ + BC→ + CA→ = 0⃗ 
(b) AB→ + BC→ – AC→ = 0⃗ 
(c) AB→ + BC→ – CA→ = 0⃗ 
(d) AB→ – CB→ + CA→ = 0⃗ 

Answer: (c) AB→ + BC→ – CA→ = 0⃗ 

Question 2.
If a⃗  and b⃗  are two collinear vectors, then which of the following are incorrect:
(a) b⃗  = λa⃗  tor some scalar λ.
(b) a⃗  = ±b⃗ 
(c) the respective components of a⃗  and b⃗  are proportional
(d) both the vectors a⃗  and b⃗  have the same direction, but different magnitudes.

Answer: (d) both the vectors a⃗  and b⃗  have the same direction, but different magnitudes.

Question 3.
If a is a non-zero vector of magnitude ‘a’ and λa non-zero scalar, then λa⃗  is unit vector if:
(a) λ = 1
(b) λ = -1
(c) a = |λ|
(d) a = 1|λ|

Answer: (d) a = 1|λ|

Question 4.
Let λ be any non-zero scalar. Then for what possible values of x, y and z given below, the vectors 2i^ – 3j^ + 4k^ and xi^ – yj^ + zk^ are perpendicular:
(a) x = 2λ. y = λ, z = λ
(b) x = λ, y = 2λ, z = -λ
(c) x = -λ, y = 2λ, z = λ
(d) x = -λ, y = -2λ, z = λ.

Answer: (c) x = -λ, y = 2λ, z = λ

Question 5.
Let the vectors a⃗  and b⃗  be such that |a⃗ | = 3 and |b⃗ | = √23, then a⃗  × b⃗  is a unit vector if the angle between a⃗  and b⃗  is:
(a) π6
(b) π4
(c) π3
(d) π2

Answer: (b) π4

Question 6.
Area of a rectangle having vertices
A(-i^ + 12 j^ + 4k^),
B(i^ + 12 j^ + 4k^),
C(i^ – 12 j^ + 4k^),
D(-i^ – 12 j^ + 4k^) is
(a) 12 square unit
(b) 1 square unit
(c) 2 square units
(d) 4 square units.

Answer: (c) 2 square units

Question 7.
If θ is the angle between two vectors a⃗ , b⃗ , then a⃗ .b⃗  ≥ 0 only when
(a) 0 < θ < π2
(b) 0 ≤ θ ≤ π2
(c) 0 < θ < π
(d) 0 ≤ θ ≤ π

Answer: (b) 0 ≤ θ ≤ π2

Question 8.
Let a⃗  and b⃗  be two unit vectors and 6 is the angle between them. Then a⃗  + b⃗  is a unit vector if:
(a) θ = π4
(b) θ = π3
(c) θ = π2
(d) θ = 2π3

Answer: (d) θ = 2π3

Question 9.
If {i^, j^, k^} are the usual three perpendicular unit vectors, then the value of:
i^.(j^ × k^) + j^.(i^ × k^) + k^.(i^ × j^) is
(a) 0
(b) -1
(c) 1
(d) 3

Answer: (d) 3

Question 10.
If θ is the angle between two vectors a⃗  and b⃗ , then |a⃗ .b⃗ | = |a⃗  × b⃗ | when θ is equal to:
(a) 0
(b) π4
(c) π2
(d) π

Answer: (b) π4

Question 11.
The area of the triangle whose adjacent sides are
a⃗  = 3i^ + j^ + 4k^ and b⃗  = i^ – j^ + k^ is
(a) 1/2 42√
(b) 42
(c) 42√
(d) 21√

Answer: (a) 1/2 42√

Question 12.
The magnitude of the vector 6i^ + 2j^ + 3k^ is
(a) 5
(b) 7
(c) 12
(d) 1.

Answer: (b) 7

Question 13.
The vector with initial point P (2, -3, 5) and terminal point Q (3, -4, 7) is
(a) i^ – j^ + 2k^
(b) 5i^ – 7j^ + 12k^
(c) –i^ + j^ – 2k^
(d) None of these.

Answer: (a) i^ – j^ + 2k^

Question 14.
The angle between the vectors i^ – j^ and j^ – k^ is
(a) π3
(b) 2π3
(c) –π3
(d) 5π6

Answer: (b) 2π3

Question 15.
The value of ‘λ’ for which the two vectors:
2i^ – j^ + 2k^ and 3i^ + λj^ + k^ are perpendicular is
(a) 2
(b) 4
(c) 6
(d) 8.

Answer: (d) 8.

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