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

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 position vector of the point (1, 0, 2) is
	A. \(\vec{i}\) +\(\vec{j}\) + 2\(\vec{k}\)
	B. \(\vec{i}\) + 2\(\vec{j}\)
	C. \(\vec{2}\) + 3\(\vec{k}\)
	D. \(\vec{i}\) + 2\(\vec{K}\)

Ans: \(\vec{i}\) + 2\(\vec{K}\)

Q2.	The modulus of 7\(\vec{i}\) – 2\(\vec{J}\) + \(\vec{K}\)
	A. \(\sqrt{10}\)
	B. \(\sqrt{55}\)
	C. 3\(\sqrt{6}\)
	D. 6

Ans: 3\(\sqrt{6}\)

Q3.	If O be the origin and \(\vec{OP}\) = 2\(\hat{i}\) + 3\(\hat{j}\) – 4\(\hat{k}\) and \(\vec{OQ}\) = 5\(\hat{i}\) + 4\(\hat{j}\) -3\(\hat{k}\), then \(\vec{PQ}\) is equal to
	A. 7\(\hat{i}\) + 7\(\hat{j}\) – 7\(\hat{k}\)
	B. -3\(\hat{i}\) + \(\hat{j}\) – \(\hat{k}\)
	C. -7\(\hat{i}\) – 7\(\hat{j}\) + 7\(\hat{k}\)
	D. 3\(\hat{i}\) + \(\hat{j}\) + \(\hat{k}\)

Ans: 3\(\hat{i}\) + \(\hat{j}\) + \(\hat{k}\)

Q4.	The scalar product of 5\(\hat{i}\) + \(\hat{j}\) – 3\(\hat{k}\) and 3\(\hat{i}\) – 4\(\hat{j}\) + 7\(\hat{k}\) is
	A. 10
	B. -10
	C. 15
	D. -15

Ans: -10

Q5.	If \(\vec{a}\).\(\vec{b}\) = 0, then
	A. a ⊥ b
	B. \(\vec{a}\) \|\| \(\vec{b}\)
	C. \(\vec{a}\) + \(\vec{b}\) = 0
	D. \(\vec{a}\) – \(\vec{b}\) = 0

Ans: a ⊥ b

Q6.	\(\vec{i}\) – \(\vec{j}\) =
	A. 0
	B. 1
	C. \(\vec{k}\)
	D. –\(\vec{k}\)

Ans: 0

Q7.	\(\vec{k}\) × \(\vec{j}\) =
	A. 0
	B. 1
	C. \(\vec{i}\)
	D. –\(\vec{i}\)

Ans: –\(\vec{i}\)

Q8.	\(\vec{a}\). \(\vec{a}\) =
	A. 0
	B. 1
	C. \|\(\vec{a}\)\|²
	D. \|\(\vec{a}\)\|

Ans: |\(\vec{a}\)|²

Q9.	The projection of the vector 2\(\hat{i}\) – \(\hat{j}\) + \(\hat{k}\) on the vector \(\hat{i}\) – 2\(\hat{j}\) + \(\hat{k}\) is
	A. \(\frac{4}{√6}\)
	B. \(\frac{5}{√6}\)
	C. \(\frac{4}{√3}\)
	D. \(\frac{7}{√6}\)

Ans: \(\frac{5}{√6}\)

Q10.	If \(\vec{a}\) = \(\vec{i}\) – \(\vec{j}\) + 2\(\vec{k}\) and b = 3\(\vec{i}\) + 2\(\vec{j}\) – \(\vec{k}\) then the value of (\(\vec{a}\) + 3\(\vec{b}\))(2\(\vec{a}\) – \(\vec{b}\))=.
	A. 15
	B. -15
	C. 18
	D. -18

Ans: -15

Q11.	If \|\(\vec{a}\)\|= \(\sqrt{26}\), \|b\| = 7 and \|\(\vec{a}\) × \(\vec{b}\)\| = 35, then \(\vec{a}\).\(\vec{b}\) =
	A. 8
	B. 7
	C. 9
	D. 12

Ans: 7

Q12.	If \(\vec{a}\) = 2\(\vec{i}\) – 3\(\vec{j}\) + 4\(\vec{k}\) and \(\vec{b}\) = \(\vec{i}\) + 2\(\vec{j}\) + \(\vec{k}\) then \(\vec{a}\) + \(\vec{b}\) =
	A. \(\vec{i}\) + \(\vec{j}\) + 3\(\vec{k}\)
	B. 3\(\vec{i}\) – \(\vec{j}\) + 5\(\vec{k}\)
	C. \(\vec{i}\) – \(\vec{j}\) – 3\(\vec{k}\)
	D. 2\(\vec{i}\) + \(\vec{j}\) + \(\vec{k}\)

Ans: 3\(\vec{i}\) – \(\vec{j}\) + 5\(\vec{k}\)

Q13.	If \(\vec{a}\) = \(\vec{i}\) + 2\(\vec{j}\) + 3\(\vec{k}\) and \(\vec{b}\) = 3\(\vec{i}\) + 2\(\vec{j}\) + \(\vec{k}\), then cos θ =
	A. \(\frac{6}{7}\)
	B. \(\frac{5}{7}\)
	C. \(\frac{4}{7}\)
	D. \(\frac{1}{2}\)

Ans: \(\frac{5}{7}\)

Q14.	If \|\(\vec{a}\) + \(\vec{b}\)\| = \|\(\vec{a}\) – \(\vec{b}\)\|, then
	A. \(\vec{a}\) \|\| \(\vec{a}\)
	B. \(\vec{a}\) ⊥ \(\vec{b}\)
	C. \|\(\vec{a}\)\| = \|\(\vec{b}\)\|
	D. None of these

Ans: \(\vec{a}\) ⊥ \(\vec{b}\)

Q15.	The projection of the vector 2\(\hat{i}\) + 3\(\hat{j}\) – 6\(\hat{k}\) on the line joining the points (3, 4, 2) and (5, 6,3) is
	A. \(\frac{2}{3}\)
	B. \(\frac{4}{3}\)
	C. –\(\frac{4}{3}\)
	D. \(\frac{5}{3}\)

Ans: \(\frac{4}{3}\)

Q16.	If \|\(\vec{a}\) × \(\vec{b}\)\| – \|\(\vec{a}\).\(\vec{b}\)\|, then the angle between \(\vec{a}\) and \(\vec{b}\), is
	A. 0
	B. \(\frac{π}{2}\)
	C. \(\frac{π}{4}\)
	D. π

Ans: \(\frac{π}{4}\)

Q17.	The angle between two vector \(\vec{a}\) and \(\vec{b}\) with magnitude √3 and 4, respectively and \(\vec{a}\).\(\vec{b}\) = 2√3 is
	A. \(\frac{π}{6}\)
	B. \(\frac{π}{3}\)
	C. \(\frac{π}{2}\)
	D. \(\frac{5π}{2}\)

Ans: \(\frac{π}{3}\)

Q18.	Unit vector perpendicular to each of the vector 3\(\hat{i}\) + \(\hat{j}\) + 2\(\hat{k}\) and 2\(\hat{i}\) – 2\(\hat{j}\) + 4\(\hat{k}\) is
	A. \(\frac{\hat{i}+\hat{j}+\hat{k}}{√3}\)
	B. \(\frac{\hat{i}-\hat{j}+\hat{k}}{√3}\)
	C. \(\frac{\hat{i}-\hat{j}-\hat{k}}{√3}\)
	D. \(\frac{\hat{i}+\hat{j}-\hat{k}}{√3}\)

Ans: \(\frac{\hat{i}-\hat{j}-\hat{k}}{√3}\)

Q19.	If \(\vec{a}\) = 2\(\vec{i}\) – 5\(\vec{j}\) + k and \(\vec{b}\) = 4\(\vec{i}\) + 2\(\vec{j}\) + \(\vec{k}\) then \(\vec{a}\).\(\vec{b}\) =
	A. 0
	B. -1
	C. 1
	D. 2

Ans: -1

Q20.	If 2\(\vec{i}\) + \(\vec{j}\) + \(\vec{k}\), 6\(\vec{i}\) – \(\vec{j}\) + 2\(\vec{k}\) and 14\(\vec{i}\) – 5\(\vec{j}\) + 4\(\vec{k}\) be the position vector of the points A, B and C respectively, then
	A. The A, B and C are collinear
	B. A, B and C are not colinear
	C. \(\vec{AB}\) ⊥ \(\vec{BC}\)
	D. None of these

Ans: The A, B and C are collinear

MCQ Questions for Class 12 Maths

NCERT Solution of Maths Class 12

Class 12 Maths

NCERT SOLUTIONS FOR CLASS 12

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-A

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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