Class 11 Mathematics Chapter 3 – Vectors MCQs | FBISE | Grade 11 Math - MCQs

Practice 50 exam-oriented MCQs covering vectors in the plane and space, vector operations, dot product and cross product for FBISE HSSC-I Mathematics.

1. A vector quantity has:

A) A) Magnitude only
B) B) Direction only
C) C) Both magnitude and direction
D) D) Neither magnitude nor direction

2. A vector is commonly represented geometrically by a:

A) A) Directed line segment
B) B) Circle
C) C) Point only
D) D) Number line only

3. Two vectors are equal if they have the same:

A) A) Direction only
B) B) Magnitude only
C) C) Magnitude and direction
D) D) Initial point only

4. A vector having zero magnitude is called the:

A) A) Unit vector
B) B) Zero or null vector
C) C) Position vector
D) D) Negative vector

5. A vector whose magnitude is 1 is called a:

A) A) Null vector
B) B) Unit vector
C) C) Parallel vector
D) D) Position vector

6. The vector $\vec{AB}$ represents a vector directed from:

A) A) B to A
B) B) A to B
C) C) Origin to A
D) D) Origin to B

7. Two non-zero vectors are parallel when they have:

A) A) Equal magnitudes only
B) B) The same or opposite directions
C) C) Perpendicular directions
D) D) Zero magnitude

8. The negative of a vector has:

A) A) The same magnitude and opposite direction
B) B) Opposite magnitude and same direction
C) C) Zero magnitude
D) D) Double the magnitude

9. The position vector of a point $P(x,y)$ is:

A) A) $x\mathbf{i}-y\mathbf{j}$
B) B) $x\mathbf{i}+y\mathbf{j}$
C) C) $y\mathbf{i}+x\mathbf{j}$
D) D) $xy(\mathbf{i}+\mathbf{j})$

10. The fundamental unit vectors in the Cartesian plane are:

A) A) $\mathbf{i}$ and $\mathbf{j}$
B) B) $\mathbf{i}$ and $\mathbf{k}$
C) C) $\mathbf{j}$ and $\mathbf{k}$
D) D) $\mathbf{i},\mathbf{j},\mathbf{k}$ only

11. In the Cartesian plane, $\mathbf{i}$ is the unit vector along the:

A) A) y-axis
B) B) x-axis
C) C) z-axis
D) D) line $y=x$

12. In the Cartesian plane, $\mathbf{j}$ is the unit vector along the:

A) A) x-axis
B) B) y-axis
C) C) z-axis
D) D) line $y=-x$

13. The vector $3\mathbf{i}+4\mathbf{j}$ has magnitude:

A) A) 5
B) B) 7
C) C) 12
D) D) 25

14. The magnitude of $a\mathbf{i}+b\mathbf{j}$ is:

A) A) $a+b$
B) B) $\sqrt{a^2+b^2}$
C) C) $a^2+b^2$
D) D) $|a-b|$

15. The unit vector in the direction of a non-zero vector $\vec{a}$ is:

A) A) $|\vec{a}|\vec{a}$
B) B) $\vec{a}/|\vec{a}|$
C) C) $\vec{a}^2$
D) D) $1/\vec{a}$

16. If $\vec{a}=6\mathbf{i}+8\mathbf{j}$ , then the unit vector in its direction is:

A) A) $\frac{3}{5}\mathbf{i}+\frac{4}{5}\mathbf{j}$
B) B) $\frac{4}{5}\mathbf{i}+\frac{3}{5}\mathbf{j}$
C) C) $6\mathbf{i}+8\mathbf{j}$
D) D) $\frac{6}{8}\mathbf{i}+\frac{8}{6}\mathbf{j}$

17. If $\vec{a}=2\mathbf{i}+3\mathbf{j}$ and $\vec{b}=4\mathbf{i}-\mathbf{j}$ , then $\vec{a}+\vec{b}$ is:

A) A) $6\mathbf{i}+2\mathbf{j}$
B) B) $2\mathbf{i}+4\mathbf{j}$
C) C) $6\mathbf{i}-4\mathbf{j}$
D) D) $8\mathbf{i}+3\mathbf{j}$

18. If $\vec{a}=5\mathbf{i}-2\mathbf{j}$ and $\vec{b}=\mathbf{i}+3\mathbf{j}$ , then $\vec{a}-\vec{b}$ is:

A) A) $4\mathbf{i}-5\mathbf{j}$
B) B) $6\mathbf{i}+\mathbf{j}$
C) C) $4\mathbf{i}+\mathbf{j}$
D) D) $5\mathbf{i}-6\mathbf{j}$

19. If $\vec{a}=2\mathbf{i}-3\mathbf{j}$ , then $3\vec{a}$ is:

A) A) $6\mathbf{i}-9\mathbf{j}$
B) B) $5\mathbf{i}-6\mathbf{j}$
C) C) $6\mathbf{i}+9\mathbf{j}$
D) D) $2\mathbf{i}-9\mathbf{j}$

20. Scalar multiplication of a vector changes its:

A) A) Magnitude and possibly direction
B) B) Direction only in every case
C) C) Initial point only
D) D) Components into scalars

21. The triangle law of vector addition states that if two vectors are represented by two sides of a triangle in succession, their sum is represented by the:

A) A) First side
B) B) Second side
C) C) Third side taken from the initial point to the final point
D) D) Perpendicular bisector

22. The parallelogram law of vector addition represents the resultant by the:

A) A) Diagonal through the common initial point
B) B) Other diagonal
C) C) Perimeter
D) D) Shorter side

23. The polygon law of vector addition is a generalization of the:

A) A) Scalar multiplication law
B) B) Triangle law
C) C) Dot product
D) D) Cross product

24. Vector addition is:

A) A) Commutative
B) B) Never commutative
C) C) Defined only in one dimension
D) D) Always zero

25. The commutative law for vectors is:

A) A) $\vec{a}+\vec{b}=\vec{a}-\vec{b}$
B) B) $\vec{a}+\vec{b}=\vec{b}+\vec{a}$
C) C) $\vec{a}+\vec{b}=\vec{a}\vec{b}$
D) D) $\vec{a}+\vec{b}=0$

26. The associative law for vector addition is:

A) A) $\vec{a}+\vec{b}+\vec{c}=\vec{a}+\vec{b}\vec{c}$
B) B) $(\vec{a}+\vec{b})+\vec{c}=\vec{a}+(\vec{b}+\vec{c})$
C) C) $\vec{a}+\vec{b}=\vec{b}-\vec{a}$
D) D) $(\vec{a}+\vec{b})\vec{c}=0$

27. The identity element for vector addition is the:

A) A) Unit vector
B) B) Zero vector
C) C) Position vector
D) D) Negative vector

28. The additive inverse of $\vec{a}$ is:

A) A) $\vec{a}$
B) B) $2\vec{a}$
C) C) $-\vec{a}$
D) D) $|\vec{a}|$

29. For any vector $\vec{a}$ , $\vec{a}+(-\vec{a})$ equals:

A) A) $\vec{a}$
B) B) $2\vec{a}$
C) C) Zero vector
D) D) Unit vector

30. Vectors in three-dimensional space are represented using the unit vectors:

A) A) $\mathbf{i},\mathbf{j}$
B) B) $\mathbf{i},\mathbf{k}$
C) C) $\mathbf{j},\mathbf{k}$
D) D) $\mathbf{i},\mathbf{j},\mathbf{k}$

31. The vector $2\mathbf{i}-3\mathbf{j}+6\mathbf{k}$ has magnitude:

A) A) 5
B) B) 7
C) C) 9
D) D) 11

32. The magnitude of $a\mathbf{i}+b\mathbf{j}+c\mathbf{k}$ is:

A) A) $a+b+c$
B) B) $\sqrt{a^2+b^2+c^2}$
C) C) $a^2+b^2+c^2$
D) D) $|a-b-c|$

33. The position vector of $P(x,y,z)$ is:

A) A) $x\mathbf{i}+y\mathbf{j}+z\mathbf{k}$
B) B) $x\mathbf{j}+y\mathbf{k}+z\mathbf{i}$
C) C) $xyz(\mathbf{i}+\mathbf{j}+\mathbf{k})$
D) D) $x+y+z$

34. If $\vec{a}=\mathbf{i}+2\mathbf{j}+2\mathbf{k}$ , then $|\vec{a}|$ is:

A) A) 2
B) B) $\sqrt{5}$
C) C) $\sqrt{8}$
D) D) 9

35. The dot product of two vectors is also called the:

A) A) Vector product
B) B) Scalar product
C) C) Cross product
D) D) Mixed product

36. For vectors $\vec{a}$ and $\vec{b}$ , the dot product is:

A) A) $|\vec{a}||\vec{b}|\sin\theta$
B) B) $|\vec{a}||\vec{b}|\cos\theta$
C) C) $|\vec{a}|+|\vec{b}|$
D) D) $|\vec{a}|-|\vec{b}|$

37. If two non-zero vectors are perpendicular, their dot product is:

A) A) 1
B) B) −1
C) C) 0
D) D) Their product

38. If $\vec{a}=2\mathbf{i}+3\mathbf{j}$ and $\vec{b}=4\mathbf{i}-\mathbf{j}$ , then $\vec{a}\cdot\vec{b}$ is:

A) A) 5
B) B) 8
C) C) 11
D) D) −5

39. The angle between two non-zero vectors $\vec{a}$ and $\vec{b}$ can be found from:

A) A) $\cos\theta=\frac{\vec{a}\cdot\vec{b}}{|\vec{a}||\vec{b}|}$
B) B) $\sin\theta=\frac{\vec{a}\cdot\vec{b}}{|\vec{a}|+|\vec{b}|}$
C) C) $\tan\theta=\frac{|\vec{a}||\vec{b}|}{\vec{a}\cdot\vec{b}}$
D) D) $\cos\theta=|\vec{a}||\vec{b}|$

40. The cross product of two vectors is also called the:

A) A) Scalar product
B) B) Vector product
C) C) Dot product
D) D) Inner sum

41. The magnitude of $\vec{a}\times\vec{b}$ is:

A) A) $|\vec{a}||\vec{b}|\cos\theta$
B) B) $|\vec{a}||\vec{b}|\sin\theta$
C) C) $|\vec{a}|+|\vec{b}|$
D) D) $|\vec{a}|-|\vec{b}|$

42. If two vectors are parallel, their cross product is:

A) A) 1
B) B) −1
C) C) Zero vector
D) D) A unit vector

43. The direction of $\vec{a}\times\vec{b}$ is perpendicular to:

A) A) $\vec{a}$ only
B) B) $\vec{b}$ only
C) C) Both $\vec{a}$ and $\vec{b}$
D) D) Neither vector

44. The cross product $\mathbf{i}\times\mathbf{j}$ is:

A) A) $\mathbf{i}$
B) B) $\mathbf{j}$
C) C) $\mathbf{k}$
D) D) $-\mathbf{k}$

45. The cross product $\mathbf{j}\times\mathbf{i}$ is:

A) A) $\mathbf{k}$
B) B) $-\mathbf{k}$
C) C) $\mathbf{i}$
D) D) $-\mathbf{i}$

46. The dot product of a vector with itself is:

A) A) $|\vec{a}|$
B) B) $|\vec{a}|^2$
C) C) 0
D) D) 1

47. If $\vec{a}\cdot\vec{b}>0$ , the angle between the two non-zero vectors is:

A) A) Acute
B) B) Right
C) C) Obtuse
D) D) Straight

48. If $\vec{a}\cdot\vec{b}<0$ , the angle between the two non-zero vectors is:

A) A) Acute
B) B) Right
C) C) Obtuse
D) D) Zero

49. The area of the parallelogram formed by vectors $\vec{a}$ and $\vec{b}$ is:

A) A) $|\vec{a}\cdot\vec{b}|$
B) B) $|\vec{a}\times\vec{b}|$
C) C) $|\vec{a}|+|\vec{b}|$
D) D) $|\vec{a}|-|\vec{b}|$

50. The area of the triangle formed by two vectors $\vec{a}$ and $\vec{b}$ is:

A) A) $|\vec{a}\times\vec{b}|$
B) B) $2|\vec{a}\times\vec{b}|$
C) C) $\frac{1}{2}|\vec{a}\times\vec{b}|$
D) D) $|\vec{a}\cdot\vec{b}|$

Explore More Class 11 Mathematics MCQs

Chapter 1 – Complex Numbers
Chapter 2 – Matrices and Determinants
Chapter 3 – Vectors
Chapter 4 – Sequences and Series
Chapter 5 – Polynomials
Chapter 6 – Permutation and Combination
Chapter 7 – Mathematical Induction and Binomial Theorem
Chapter 8 – Fundamentals of Trigonometry
Chapter 9 – Trigonometric Functions

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Syllabus & SLO Alignment

Syllabus coverage: This chapter covers vectors in the plane and space, fundamental vector definitions, unit and null vectors, position and parallel vectors, vector addition and subtraction, triangle, parallelogram and polygon laws, scalar multiplication, vector components and magnitude, properties of vector addition, dot (scalar) product and cross (vector) product.

SLO alignment: The MCQs focus on representing vectors analytically, using the fundamental unit vectors i, j and k, finding magnitudes and unit vectors, working with vector addition and its properties, and applying dot and cross products to determine angles, perpendicularity and geometric areas. These areas are included in the FBISE/National Curriculum HSSC-I Mathematics vectors content.

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