Vector|| Class 11 || IOE || CEE || Physics

Saugat Sapkota

Class 11 || Vector|| IOE || CEE - Saugat Sapkota



1. A vector that has a magnitude but no direction is called a:
  • a) Scalar
  • b) Unit vector
  • c) Position vector
  • d) Null vector

2. The dot product of two vectors is:

  • a) A scalar
  • b) A vector
  • c) A tensor
  • d) A matrix

3. If A⃗⋅B⃗=0\vec{A} \cdot \vec{B} = 0, the vectors A⃗\vec{A} and B⃗\vec{B} are:

  • a) Parallel
  • b) Perpendicular
  • c) Equal
  • d) Opposite

4. The cross product of two vectors is:

  • a) A scalar
  • b) A vector
  • c) A scalar when vectors are parallel
  • d) A matrix

5. Which of the following is not a vector quantity?

  • a) Displacement
  • b) Velocity
  • c) Work
  • d) Force

6. The magnitude of a unit vector is:

  • a) 0
  • b) 1
  • c) Infinite
  • d) Depends on the vector

7. The position vector of a point P(x, y, z) is represented as:

  • a) xi^+yj^+zk^x \hat{i} + y \hat{j} + z \hat{k}
  • b) xk^+yi^+zj^x \hat{k} + y \hat{i} + z \hat{j}
  • c) yi^+zj^+xk^y \hat{i} + z \hat{j} + x \hat{k}
  • d) zi^+xj^+yk^z \hat{i} + x \hat{j} + y \hat{k}

8. Two vectors are said to be collinear if:

  • a) They are perpendicular to each other
  • b) They lie along the same line or parallel lines
  • c) Their magnitudes are equal
  • d) Their dot product is zero

9. The resultant of two vectors A⃗\vec{A} and B⃗\vec{B} can be found using:

  • a) Pythagoras theorem
  • b) Triangle law of vector addition
  • c) Parallelogram law of vector addition
  • d) All of the above

10. A vector having the same direction as a given vector but unit magnitude is called:

  • a) A scalar multiple
  • b) A unit vector
  • c) A perpendicular vector
  • d) A null vector

11. The scalar product of two vectors depends on:

  • a) The magnitudes of the vectors only
  • b) The angle between the vectors
  • c) The direction of the vectors only
  • d) Both the magnitudes and the angle between the vectors

12. The vector product of two parallel vectors is:

  • a) Zero
  • b) Maximum
  • c) A unit vector
  • d) None of the above

13. If the vector A⃗=2i^+3j^+4k^\vec{A} = 2 \hat{i} + 3 \hat{j} + 4 \hat{k}, the magnitude of the vector is:

  • a) 2\sqrt{2}
  • b) 99
  • c) 2929
  • d) 29\sqrt{29}

14. The angle between two vectors is 90°. What is their dot product?

  • a) 0
  • b) 1
  • c) -1
  • d) Depends on the magnitude of the vectors

15. Two vectors are perpendicular if their dot product is:

  • a) Maximum
  • b) Minimum
  • c) Zero
  • d) None of the above

16. Which one of the following is not a vector?

  • a) Momentum
  • b) Energy
  • c) Acceleration
  • d) Displacement

17. Which is the correct formula for the dot product of two vectors A⃗\vec{A} and B⃗\vec{B}?

  • a) A⃗⋅B⃗=ABcos⁡θ\vec{A} \cdot \vec{B} = AB \cos \theta
  • b) A⃗⋅B⃗=ABsin⁡θ\vec{A} \cdot \vec{B} = AB \sin \theta
  • c) A⃗⋅B⃗=ABtan⁡θ\vec{A} \cdot \vec{B} = AB \tan \theta
  • d) A⃗⋅B⃗=ABcos⁡θ\vec{A} \cdot \vec{B} = \frac{AB}{\cos \theta}

18. The magnitude of the cross product of two vectors is:

  • a) ABcos⁡θAB \cos \theta
  • b) ABsin⁡θAB \sin \theta
  • c) ABtan⁡θAB \tan \theta
  • d) ABcos⁡θ\frac{AB}{\cos \theta}

19. The projection of vector A⃗\vec{A} on vector B⃗\vec{B} is given by:

  • a) A⃗⋅B⃗∣A⃗∣\frac{\vec{A} \cdot \vec{B}}{|\vec{A}|}
  • b) A⃗⋅B⃗∣B⃗∣\frac{\vec{A} \cdot \vec{B}}{|\vec{B}|}
  • c) B⃗⋅A⃗∣B⃗∣\frac{\vec{B} \cdot \vec{A}}{|\vec{B}|}
  • d) ∣A⃗∣∣B⃗∣A⃗⋅B⃗\frac{|\vec{A}| |\vec{B}|}{\vec{A} \cdot \vec{B}}

20. Which of the following is the correct representation of the cross product A⃗×B⃗\vec{A} \times \vec{B}?

  • a) ABsin⁡θn^AB \sin \theta \hat{n}
  • b) ABcos⁡θn^AB \cos \theta \hat{n}
  • c) A2+B2A^2 + B^2
  • d) ABn^AB \hat{n}

21. The vector equation of a line passing through the point P1(x1,y1,z1)P_1(x_1, y_1, z_1) and parallel to the vector A⃗\vec{A} is:

  • a) r⃗=r⃗0+tA⃗\vec{r} = \vec{r}_0 + t \vec{A}
  • b) r⃗=tA⃗\vec{r} = t \vec{A}
  • c) r⃗=r⃗0−tA⃗\vec{r} = \vec{r}_0 - t \vec{A}
  • d) r⃗=t(r⃗0+A⃗)\vec{r} = t (\vec{r}_0 + \vec{A})

22. What is the result of the scalar triple product A⃗⋅(B⃗×C⃗)\vec{A} \cdot (\vec{B} \times \vec{C})?

  • a) A scalar quantity
  • b) A vector quantity
  • c) Zero
  • d) None of the above

23. The area of the parallelogram formed by two vectors A⃗\vec{A} and B⃗\vec{B} is given by:

  • a) ∣A⃗×B⃗∣|\vec{A} \times \vec{B}|
  • b) ∣A⃗⋅B⃗∣|\vec{A} \cdot \vec{B}|
  • c) ∣A⃗+B⃗∣|\vec{A} + \vec{B}|
  • d) ∣A⃗−B⃗∣|\vec{A} - \vec{B}|

24. The direction cosines of a vector are the cosines of the angles made by the vector with:

  • a) The three coordinate axes
  • b) The x-axis only
  • c) The z-axis only
  • d) The y-axis only

25. The vector quantity that represents rotational effect is called:

  • a) Torque
  • b) Moment of inertia
  • c) Angular momentum
  • d) Velocity

26. What is the magnitude of the resultant of two vectors A⃗\vec{A} and B⃗\vec{B} at an angle θ\theta?

  • a) A2+B2+2ABcos⁡θ\sqrt{A^2 + B^2 + 2AB \cos \theta}
  • b) A+BA + B
  • c) A−BA - B
  • d) A2+B2−2ABcos⁡θ\sqrt{A^2 + B^2 - 2AB \cos \theta}

27. The position vector of the midpoint of the line joining two points A⃗\vec{A} and B⃗\vec{B} is:

  • a) A⃗+B⃗2\frac{\vec{A} + \vec{B}}{2}
  • b) A⃗−B⃗2\frac{\vec{A} - \vec{B}}{2}
  • c) A⃗+B⃗\vec{A} + \vec{B}
  • d) A⃗−B⃗\vec{A} - \vec{B}

28. The torque on a particle due to a force F⃗\vec{F} is given by:

  • a) r⃗×F⃗\vec{r} \times \vec{F}
  • b) (\vec{r} \

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