Brainscape's Knowledge GenomeTM


Top Flashcards (Certified)
All Flashcards

Class 11 IIT JEE Prep > Vectors > Flashcards

Vectors Flashcards

(59 cards)

Start Studying
1
Q

What are the two classifications of physical quantities?

A

Scalars and vectors

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

What do scalar quantities have?

A

Only magnitude but no direction

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Give three examples of scalar quantities.

A
  • Time
  • Mass
  • Distance
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What sign can scalar quantities have?

A

Only positive or negative sign

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

What do vector quantities have?

A

Both magnitude and direction

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

How is a vector denoted?

A

As a or a

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

Give three examples of vector quantities.

A
  • Force
  • Velocity
  • Displacement
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

What does ‘a’ or ‘AB’ denote in terms of vectors?

A

Magnitude of the vector

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

What is scalar multiplication of a vector?

A

If a is a vector, then ka is a vector in the same direction as a if k>0 and magnitude is kx |a|

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

What happens to the vector ka if k<0?

A

It is opposite to a but magnitude is kx |a|

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

What is vector addition?

A

Combining vectors considering both magnitude and direction

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

What are parallel vectors?

A

Two or more vectors that can be directly added or subtracted like a scalar quantity

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

Is scalar addition similar to vector addition?

A

True, scalar addition is easier because it doesn’t involve direction

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

Fill in the blank: Scalar quantities have _______ but no direction.

A

only magnitude

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

Fill in the blank: Vector quantities are denoted as _______.

A

a or a

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

What is one method for adding two vectors?

A

Parallelogram of addition

This method visualizes the addition of two vectors as the diagonal of a parallelogram formed by the vectors.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

What does the Parallelogram Law of addition state?

A

R = (b sin θ)² + (a + b cos θ)²

This formula is used to calculate the magnitude of the resultant vector R.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

What is the alternative representation of the resultant in the Parallelogram Law?

A

R = √(a² + b² + 2ab cos θ)

This form is useful for understanding the relationship between the magnitudes of the vectors and the angle between them.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

What is the definition of the resultant of vectors?

A

The sum of vectors

The resultant vector combines the effects of the individual vectors.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

How is the angle between two vectors denoted?

A

θ = angle between two vectors

This angle is critical for determining the resultant’s magnitude and direction.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

What is the formula to find the angle a with vector a?

A

tan a = (b sin θ) / (b cos θ)

This formula relates the components of the vectors to find the angle.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

How is the magnitude of a vector represented?

A

|a| or a

The magnitude represents the length or size of the vector.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

What is the significance of the heads or tails in vectors?

A

The angle between two vectors is the angle between their heads or tails

This definition helps visualize the orientation of vectors in space.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

Fill in the blank: The magnitude of the resultant vector is given by _______.

Study These Flashcards
A

R = √(a² + b² + 2ab cos θ)

This formula calculates the resultant’s magnitude based on the individual vectors and the angle between them.

25
In vector notation, how is the difference of vectors expressed?
a - b = a + (-b) ## Footnote This shows that vector subtraction can be viewed as adding the negative of a vector.
26
What does the term 'magnitude of a' refer to?
It is the length or size of vector a ## Footnote Magnitude is a scalar value representing how strong or large the vector is.
27
What is the formula used to find the magnitude of the resultant R?
R = √(a² + b² + 2ab cosθ) ## Footnote This formula combines the magnitudes of two vectors a and b and the angle θ between them.
28
How is the direction of the resultant R determined?
tan(θ) = bcosθ / (a + bcosθ) ## Footnote This equation relates the components of the vectors to find the angle of the resultant.
29
What is the resultant force R in the given illustration?
R = √(37 N) ## Footnote The calculation shows that the resultant force has a magnitude of 37 N.
30
In the context of vector addition, what does 'a' represent?
'a' represents the magnitude of the first vector ## Footnote This is a fundamental component in calculating the resultant vector.
31
In the context of vector addition, what does 'b' represent?
'b' represents the magnitude of the second vector ## Footnote This is another fundamental component in calculating the resultant vector.
32
Fill in the blank: The resultant force R is calculated using the formula R = _______.
√(a² + b² + 2ab cosθ) ## Footnote This formula combines the magnitudes of two vectors and the angle between them.
33
What is the significance of the angle θ in vector addition?
θ is the angle between the two vectors a and b ## Footnote It affects the magnitude of the resultant vector based on the cosine component.
34
What is the formula for tan o in the resolution of a vector?
tan o = (3 - sin 53°) / (4 + 3 - cos 53°) ## Footnote This formula represents the tangent of the angle in terms of the sine and cosine of that angle.
35
What can any vector be resolved into?
Two perpendicular components ## Footnote This means that any vector can be broken down into two components that are at right angles to each other.
36
What must be true about the two components of a vector?
They must be perpendicular to each other ## Footnote This is a fundamental principle in vector resolution.
37
If a vector makes an angle 0 with a direction, what is its component in that direction?
a cos(0) ## Footnote This represents the horizontal component of the vector.
38
How can the original vector be described in relation to its components?
The original vector must lie between the two components ## Footnote This ensures that the components accurately represent the vector's direction and magnitude.
39
What is the relationship between sin 37° and cos 53°?
sin 37° = cos 53° = 3/5 ## Footnote This is an example of the complementary angle relationship in trigonometry.
40
What is the value of sin 53° and cos 37°?
sin 53° = cos 37° = 4/5 ## Footnote This shows the equality between sine and cosine of complementary angles.
41
Fill in the blank: Just like a vector can be resolved into two perpendicular components, the two perpendicular components can be ______ to get the original vector.
added ## Footnote This emphasizes the concept of vector addition using components.
42
True or False: All the tails of the vectors must meet when resolving vectors.
True ## Footnote This is a method used in vector addition to ensure accurate representation.
43
What is the significance of the angle made by the vector in terms of its components?
It determines the magnitude of the components ## Footnote The angle affects how much of the vector lies in each direction.
44
What is the most frequently used concept of vectors in physics?
Resolution of vectors ## Footnote Resolution of vectors involves breaking down vectors into their x and y components to find the resultant vector.
45
How can more than two vectors be resolved?
Each vector can be resolved in x-y direction ## Footnote This method allows for the calculation of the resultant vector from multiple vectors.
46
What is the resultant vector when adding vectors of 20 N at an angle of 53°?
Resultant = V17+42 ## Footnote The calculation involves using trigonometric functions to resolve the vector into its components.
47
What does the Polygon Law of Addition state?
Put the tail of one vector on the head of the other and join initial point to final point ## Footnote This method visually represents vector addition and helps in finding the resultant vector.
48
What is the resultant of vectors that perfectly cancel each other out?
Zero vector ## Footnote This occurs when two or more vectors are equal in magnitude but opposite in direction.
49
Fill in the blank: The mathematical representation of adding multiple vectors is R = _______.
a + b + c + d ## Footnote This formula illustrates the vector addition of multiple components.
50
What happens when vectors form a closed structure?
The resultant is zero ## Footnote For example, three vectors forming a triangle result in zero, while vectors along the sides do not.
51
What is a unit vector?
A vector of magnitude one ## Footnote Represented with a cap (^) symbol.
52
What are the standard unit vectors in physics?
* i: unit vector in positive x-direction * j: unit vector in positive y-direction * k: unit vector in positive z-direction ## Footnote These are used to express vectors mathematically.
53
How can a vector be expressed mathematically?
a = ai + bj + ck ## Footnote Where a, b, and c are the components along x, y, and z directions respectively.
54
What is the significance of the equation cos a + cos B + cos y = 1?
It relates the direction cosines of a vector ## Footnote This equation holds true for any vector in three-dimensional space.
55
What is the relationship between the components of a vector and its magnitude?
Magnitude cannot be negative ## Footnote The magnitude of a vector is always a non-negative value.
56
Fill in the blank: The x component of a vector is represented as _______.
a_x
57
Fill in the blank: The y and z components of a vector are represented as _______ and _______ respectively.
a_y, a_z
58
True or False: The magnitude of a vector can be negative.
False
59
What is the general formula for the magnitude of a vector in three-dimensional space?
Magnitude = √(a_x² + a_y² + a_z²) ## Footnote This formula calculates the length of the vector from its components.

Class 11 IIT JEE Prep (1 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2025 Bold Learning Solutions. Terms and Conditions