MCQ Questions for Class 12 Maths Chapter 10 Vector Algebra with Answers Set-C

Vector Algebra Class 12 Maths MCQs Questions with Answers

Check the below NCERT MCQ Questions for Class 12 Maths Chapter 10 Vector Algebra with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have Provided Vector Algebra Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

Class 12 Maths Chapter 10 Quiz

Class 12 Maths Chapter 10 MCQ Online Test

You can refer to NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra to revise the concepts in the syllabus effectively and improve your chances of securing high marks in your board exams.

Vector Algebra Class 12 Maths MCQ online test

Q1.	The vector having, initial and terminal points as (2, 5, 0) and (- 3, 7, 4) respectively is
	A. –\(\hat{i}\) + 12\(\hat{j}\) + 4\(\hat{k}\)
	B. 5\(\hat{i}\) + 2\(\hat{j}\) – 4\(\hat{k}\)
	C. -5\(\hat{i}\) + 2\(\hat{j}\) + 4\(\hat{k}\)
	D. \(\hat{i}\) + \(\hat{j}\) + \(\hat{k}\)

Ans: -5\(\hat{i}\) + 2\(\hat{j}\) + 4\(\hat{k}\)

Q2.	Find the value of λ such that the vectors \(\vec{a}\) = 2\(\hat{i}\) + λ\(\hat{j}\) + \(\hat{k}\) and \(\vec{b}\) = \(\hat{i}\) + 2\(\hat{j}\) + 3\(\hat{k}\) are orthogonal
	A. 0
	B. 1
	C. \(\frac{3}{2}\)
	D. –\(\frac{5}{2}\)

Ans: –\(\frac{5}{2}\)

Q3.	The value of λ for which the vectors 3\(\hat{i}\) – 6\(\hat{j}\) + \(\hat{k}\) and 2\(\hat{i}\) – 4\(\hat{j}\) + λ\(\hat{k}\) are parallel is
	A. \(\frac{2}{3}\)
	B. \(\frac{3}{2}\)
	C. \(\frac{5}{2}\)
	D. –\(\frac{2}{5}\)

Ans: \(\frac{2}{3}\)

Q4.	The vectors from origin to the points A and B are \(\vec{a}\) = 2\(\hat{i}\) – 3\(\hat{j}\) +2\(\hat{k}\) and \(\vec{b}\) = 2\(\hat{i}\) + 3\(\hat{j}\) + \(\hat{k}\) respectively, then the area of triangle OAB is
	A. 340
	B. \(\sqrt{25}\)
	C. \(\sqrt{229}\)
	D. \(\frac{1}{2}\) \(\sqrt{229}\)

Ans: \(\frac{1}{2}\) \(\sqrt{229}\)

Q5.	For any vector \(\vec{a}\) the value of (\(\vec{a}\) × \(\vec{i}\))² + (\(\vec{a}\) × \(\hat{j}\))² + (\(\vec{a}\) × \(\hat{k}\))² is equal to
	A. \(\vec{a}\)²
	B. 3\(\vec{a}\)²
	C. 4\(\vec{a}\)²
	D. 2\(\vec{a}\)²

Ans: 2\(\vec{a}\)²

Q6.	If \|\(\vec{a}\)\| = 10, \|\(\vec{b}\)\| = 2 and \(\vec{a}\).\(\vec{b}\) = 12, then the value of \|\(\vec{a}\) × \(\vec{b}\)\| is
	A. 5
	B. 10
	C. 14
	D. 16

Ans: 16

Q7.	The vectors λ\(\hat{i}\) + \(\hat{j}\) + 2\(\hat{k}\), \(\hat{i}\) + λ\(\hat{j}\) – \(\hat{k}\) and 2\(\hat{i}\) – \(\hat{j}\) + λ\(\hat{k}\) are coplanar if
	A. λ = -2
	B. λ = 0
	C. λ = 1
	D. λ = -1

Ans: λ = -2

Q8.	If \(\vec{a}\), \(\vec{b}\), \(\vec{c}\) are unit vectors such that \(\vec{a}\) + \(\vec{b}\) + \(\vec{c}\) = \(\vec{0}\), then the value of \(\vec{a}\).\(\vec{b}\) + \(\vec{b}\).\(\vec{c}\) + \(\vec{c}\).\(\vec{a}\)
	A. 1
	B. 3
	C. –\(\frac{3}{2}\)
	D. None of these

Ans: –\(\frac{3}{2}\)

Q9.	Projection vector of \(\vec{a}\) on \(\vec{b}\) is
	A. (\(\frac{\vec{a}.\vec{b}}{\|\vec{b}\|^2}\))\(\vec{b}\)
	B. \(\frac{\vec{a}.\vec{b}}{\|\vec{b}\|}\)
	C. \(\frac{\vec{a}.\vec{b}}{\|\vec{a}\|}\)
	D. (\(\frac{\vec{a}.\vec{b}}{\|\vec{a}\|^2}\))\(\hat{b}\)

Ans: \(\frac{\vec{a}.\vec{b}}{|\vec{b}|}\)

Q10.	If \(\vec{a}\), \(\vec{b}\), \(\vec{c}\) are three vectors such that \(\vec{a}\) + \(\vec{b}\) + \(\vec{c}\) = 5 and \|\(\vec{a}\)\| = 2, \|\(\vec{b}\)\| = 3, \|\(\vec{c}\)\| = 5, then the value of \(\vec{a}\).\(\vec{b}\) +\(\vec{b}\).\(\vec{c}\) + \(\vec{c}\).\(\vec{a}\) is
	A. 0
	B. 1
	C. -19
	D. 38

Ans: -19

Q11.	If \|\(\vec{a}\)\| 4 and – 3 ≤ λ ≤ 2, then the range of \|λ\(\vec{a}\)\| is
	A. [0, 8]
	B. [-12, 8]
	C. [0, 12]
	D. [8, 12]

Ans: [-12, 8]

Q12.	The number of vectors of unit length perpendicular to the vectors \(\vec{a}\) = 2\(\hat{i}\) + \(\hat{j}\) + 2\(\hat{k}\) and \(\vec{b}\) = \(\hat{j}\) + \(\hat{k}\) is
	A. one
	B. two
	C. three
	D. infinite

Ans: two

Q13.	If (\(\frac{1}{2}\), \(\frac{1}{3}\), n) are the direction cosines of a line, then the value of n is
	A. \(\frac{\sqrt{23}}{6}\)
	B. \(\frac{23}{6}\)
	C. \(\frac{2}{3}\)
	D. –\(\frac{3}{2}\)

Ans: \(\frac{\sqrt{23}}{6}\)

Q14.	Find the magnitude of vector 3\(\hat{i}\) + 2\(\hat{j}\) + 12\(\hat{k}\)
	A. \(\sqrt{157}\)
	B. 4\(\sqrt{11}\)
	C. \(\sqrt{213}\)
	D. 9√3

Ans: \(\sqrt{157}\)

Q15.	Three points (2, -1, 3), (3, – 5, 1) and (-1, 11, 9) are
	A. Non-collinear
	B. Non-coplanar
	C. Collinear
	D. None of these

Ans: Collinear

Q16.	The vectors 3\(\hat{i}\) + 5\(\hat{j}\) + 2\(\hat{k}\), 2\(\hat{i}\) – 3\(\hat{j}\) – 5\(\hat{k}\) and 5\(\hat{i}\) + 2\(\hat{j}\) – 3\(\hat{k}\) form the sides of
	A. Isosceles triangle
	B. Right triangle
	C. Scalene triangle
	D. Equilateral triangle

Ans: Isosceles triangle

Q17.	The points with position vectors 60\(\hat{i}\) + 3\(\hat{j}\), 40\(\hat{i}\) – 8\(\hat{j}\) and a\(\hat{i}\) – 52\(\hat{j}\) are collinear if
	A. a = -40
	B. a = 40
	C. a = 20
	D. None of these

Ans: a = -40

Q18.	The ratio in which 2x + 3y + 5z = 1 divides the line joining the points (1, 0, -3) and (1, -5, 7) is
	A. 5 : 3
	B. 3 : 2
	C. 2 : 1
	D. 1 : 3

Ans: 5 : 3

Q19.	If O is origin and C is the mid point of A (2, -1) and B (-4, 3) then the value of \(\bar{OC}\) is
	A. \(\hat{i}\) + \(\hat{j}\)
	B. \(\hat{i}\) – \(\hat{j}\)
	C. –\(\hat{i}\) + \(\hat{j}\)
	D. –\(\hat{i}\) – \(\hat{j}\)

Ans: –\(\hat{i}\) + \(\hat{j}\)

Q20.	If ABCDEF is regular hexagon, then \(\vec{AD}\) + \(\vec{EB}\) + \(\vec{FC}\) is equal
	A. 0
	B. 2\(\vec{AB}\)
	C. 3\(\vec{AB}\)
	D. 4\(\vec{AB}\)

Ans: 4\(\vec{AB}\)

MCQ Questions for Class 12 Maths

NCERT Solution of Maths Class 12

Class 12 Maths

NCERT SOLUTIONS FOR CLASS 12

Q9.	Projection vector of \(\vec{a}\) on \(\vec{b}\) is
	A. (\(\frac{\vec{a}.\vec{b}}{\|\vec{b}\|^2}\))\(\vec{b}\)
	B. \(\frac{\vec{a}.\vec{b}}{\|\vec{b}\|}\)
	C. \(\frac{\vec{a}.\vec{b}}{\|\vec{a}\|}\)
	D. (\(\frac{\vec{a}.\vec{b}}{\|\vec{a}\|^2}\))\(\hat{b}\)

MCQ Questions for Class 12 Maths Chapter 10 Vector Algebra with Answers

MCQ Questions for Class 12 Maths Chapter 10 Vector Algebra with Answers Set-C

Vector Algebra Class 12 Maths MCQs Questions with Answers

Class 12 Maths Chapter 10 Quiz

Class 12 Maths Chapter 10 MCQ Online Test

Vector Algebra Class 12 Maths MCQ online test

MCQ Questions for Class 12 Maths

NCERT Solution of Maths Class 12

Class 12 Maths

NCERT Solution of Maths Class 12 Chapter 1

NCERT Solution of Maths Class 12 Chapter 2

NCERT Solution of Maths Class 12 Chapter 3

NCERT Solution of Maths Class 12 Chapter 4

NCERT Solution of Maths Class 12 Chapter 5

NCERT Solution of Maths Class 12 Chapter 6

NCERT Solution of Maths Class 12 Chapter 7

NCERT Solution of Maths Class 12 Chapter 8

NCERT Solution of Maths Class 12 Chapter 9

NCERT Solution of Maths Class 12 Chapter 10

NCERT Solution of Maths Class 12 Chapter 11

NCERT Solution of Maths Class 12 Chapter 12

NCERT Solution of Maths Class 12 Chapter 13

MCQ QUESTIONS WITH ANSWER

NCERT SOLUTIONS FOR CLASS 12

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