Hello, future educators! As you gear up for the
Haryana Teacher Eligibility Test (HTET) 2023, mastering the concept of vectors
is essential. In this comprehensive blog, we will embark on a journey to
demystify vectors, helping you grasp the intricacies of direction and magnitude
and preparing you effectively for the upcoming exam. Vectors are a vital
component of the science curriculum in HTET, whether you aspire to become a
primary teacher, a trained graduate teacher (TGT), or a postgraduate teacher
(PGT). Let's explore the world of vectors together and ensure your success in
the exam!
1. What is a vector quantity?
a) A quantity with only magnitude
b) A quantity with both magnitude and direction
c) A quantity with no magnitude
d) A quantity with no direction
2. Which of the following is an example of a scalar quantity?
a) Velocity
b) Force
c) Temperature
d) Displacement
3. In vector addition, when two vectors are added together, the result is called the:
a) Sum
b) Difference
c) Scalar
d) Magnitude
4. If two vectors are parallel and pointing in the same direction, their resultant will have:
a) Greater magnitude
b) Lesser magnitude
c) Zero magnitude
d) Negative magnitude
5. Which mathematical operation is used to find the magnitude of a vector?
a) Addition
b) Subtraction
c) Dot product
d) Square root
6. When adding two vectors, if they are at right angles to each other, the magnitude of the resultant is equal to:
a) The sum of the magnitudes of the vectors
b) The difference between the magnitudes of the vectors
c) The square root of the sum of the squares of the magnitudes
d) Zero
7. Which vector operation results in a scalar quantity?
a) Dot product
b) Cross product
c) Vector addition
d) Scalar multiplication
8. Two vectors are said to be collinear if:
a) They have the same magnitude
b) They have opposite directions
c) They have different magnitudes
d) They lie along the same straight line
9. The magnitude of a vector can never be:
a) Zero
b) Negative
c) Greater than its components
d) Greater than the sum of its components
10. Which of the following is a unit vector in the y-direction?
a) i
b) j
c) k
d) √2i + √2j
11. Which of the following is a true statement about vector subtraction?
a) The order of subtraction does not matter for vectors.
b) Vector subtraction is the same as vector addition.
c) To subtract two vectors, reverse the direction of the second vector and then add them.
d) Vector subtraction is not defined.
12. The dot product of two vectors results in a scalar quantity and is also known as:
a) Cross product
b) Magnitude
c) Scalar product
d) Vector addition
13. Which of the following is a vector quantity?
a) Speed
b) Distance
c) Displacement
d) Temperature
14. If the angle between two vectors is 90 degrees, the dot product of these vectors is:
a) Zero
b) Equal to the product of their magnitudes
c) Negative
d) Undefined
15. Which of the following vector operations is distributive over addition?
a) Scalar multiplication
b) Cross product
c) Dot product
d) Vector subtraction
16. When you multiply a vector by a positive scalar, the direction of the resulting vector:
a) Remains the same
b) Reverses
c) Becomes undefined
d) Depends on the specific scalar used
17. Which vector operation results in a vector perpendicular to both of the original vectors?
a) Dot product
b) Scalar multiplication
c) Vector addition
d) Cross product
18. If two vectors are collinear and have the same direction, their dot product is:
a) Zero
b) Negative
c) Positive
d) Undefined
19. The magnitude of a vector is always:
a) Positive
b) Negative
c) Zero
d) Positive or negative, depending on the direction
20. When you add two vectors, and the result is zero, the vectors are said to be:
a) Perpendicular
b) Collinear and in opposite directions
c) Collinear and in the same direction
d) Orthogonal
21. The dot product of two perpendicular vectors is:
a) Zero
b) Negative
c) Equal to the product of their magnitudes
d) Undefined
22. Which of the following operations can be used to determine the angle between two vectors?
a) Cross product
b) Dot product
c) Scalar multiplication
d) Vector addition
23. If the magnitude of vector A is greater than the magnitude of vector B, and the angle between them is 90 degrees, what can you conclude about their dot product (A ⋅ B)?
a) It's greater than zero
b) It's less than zero
c) It's equal to zero
d) It's undefined
24. A vector has a magnitude of 8 units and points east. What is the x-component of this vector?
a) 8
b) -8
c) 0
d) Undefined
25. Given two vectors A and B, if the cross product A × B results in a zero vector, what can you conclude about the angle between them?
a) They are perpendicular.
b) They are parallel.
c) They have a 45-degree angle between them.
d) They have a 90-degree angle between them.
26. Which of the following operations is used to calculate the torque produced by a force acting on a lever arm?
a) Dot product
b) Cross product
c) Scalar multiplication
d) Vector addition
27. If vector A is multiplied by a scalar k, and the result is a vector with the same direction as A but a magnitude of 3 times that of A, what is the value of k?
a) 3
b) 0
c) 1/3
d) -3
28. The magnitude of the cross product of two vectors is equal to:
a) The product of their magnitudes
b) The sum of their magnitudes
c) The difference of their magnitudes
d) The square of their magnitudes
29. If two vectors A and B are collinear, the cross product A × B is equal to:
a) Zero
b) The product of their magnitudes
c) Undefined
d) The sum of their magnitudes
30. The cross product of two vectors results in a vector that is:
a) Parallel to the plane formed by the original vectors
b) Perpendicular to the plane formed by the original vectors
c) Collinear with one of the original vectors
d) Undefined
31. If vector A is added to its negative vector (-A), what is the resultant vector?
a) The resultant is zero.
b) The resultant is twice the magnitude of A.
c) The resultant is A itself.
d) The resultant is undefined.
32. Which of the following vectors has the same magnitude as vector A but points in the opposite direction?
a) Vector B = -A
b) Vector C = A
c) Vector D = 2A
d) Vector E = A/2
33. In a right triangle, the longest side is called the:
a) Adjacent side
b) Hypotenuse
c) Opposite side
d) None of the above
34. If two vectors have the same magnitude and are at an angle of 180 degrees to each other, what can you conclude about their dot product?
a) It's greater than zero.
b) It's less than zero.
c) It's equal to zero.
d) It's undefined.
35. When multiplying two vectors, the result is:
a) A scalar quantity
b) A vector quantity
c) A complex number
d) Always zero.
36. Which vector operation is distributive over vector addition?
a) Scalar multiplication
b) Dot product
c) Cross product
d) Vector subtraction
37. What is the angle between the x-axis and the resultant vector when adding two vectors with different angles with respect to the x-axis?
a) The average of the two angles
b) The sum of the two angles
c) The difference of the two angles
d) It cannot be determined without additional information.
38. The vector sum of two vectors can be obtained graphically using which method?
a) Parallelogram rule
b) Right-hand rule
c) Pythagorean theorem
d) Algebraic addition
39. If you add a vector A to its negative vector (-A), what is the result?
a) A vector with double the magnitude of A
b) A zero vector
c) A vector with magnitude zero
d) A vector with magnitude A
40. Which of the following vectors has the same direction as vector A but a magnitude of 1?
a) Vector B = A
b) Vector C = -A
c) Vector D = 2A
d) Vector E = A/|A|
41. Which of the following statements is true regarding the cross product of two vectors?
a) The result is a scalar quantity.
b) The result is commutative.
c) The result is a vector perpendicular to the plane formed by the original vectors.
d) The result is always zero.
42. The dot product of two vectors is used to calculate:
a) The magnitude of the resultant vector.
b) The angle between the vectors.
c) A vector perpendicular to both vectors.
d) The vector sum of the two vectors.
43. If you have two vectors A and B, and their cross product A × B is a zero vector, what does this imply about the vectors A and B?
a) They are parallel.
b) They are perpendicular.
c) They are collinear.
d) They are antiparallel.
44. Which of the following operations between vectors results in a scalar quantity?
a) Cross product
b) Dot product
c) Vector addition
d) Scalar multiplication
45. When you multiply a vector by a scalar, what happens to the direction of the vector?
a) It remains unchanged.
b) It reverses.
c) It becomes undefined.
d) It becomes perpendicular to the original vector.
46. The magnitude of a vector can never be:
a) Greater than its components.
b) Less than its components.
c) Negative.
d) Zero.
47. What is the unit vector along the positive x-axis in a 3D coordinate system?
a) i
b) j
c) k
d) None of the above.
48. The cross product of two vectors is represented by which mathematical operation?
a) Division
b) Multiplication
c) Dot (·)
d) Cross (×)
49. When two vectors are added together, the resultant vector lies in the same plane as the original vectors. This statement exemplifies which vector addition property?
a) Commutative
b) Associative
c) Parallelogram law
d) Distributive
50. In a 3D Cartesian coordinate system, what are the three mutually perpendicular unit vectors corresponding to the x, y, and z axes, respectively?
a) i, j, k
b) u, v, w
c) x, y, z
d) a, b, c
As we conclude this MCQ-based guide on vectors for
HTET 2023, we trust that you've gained the knowledge and confidence needed to
tackle vector-related questions in the exam. Vectors are a fundamental concept
in science and an indispensable part of an educator's toolkit. To excel,
practice rigorously, revisit the concepts covered here, and stay updated with
any changes to the HTET syllabus. Your dedication and preparation will surely
lead to success when you walk into the examination hall. Best of luck on your
HTET 2023 journey, and may you soon embark on a fulfilling career in education.
Keep your passion for learning alive and continue to inspire future
generations!
No comments:
Post a Comment