Podcast
Questions and Answers
Which statement about the unit vectors iˆ, ˆj, and kˆ is incorrect?
Which statement about the unit vectors iˆ, ˆj, and kˆ is incorrect?
- iˆ  ˆj = kˆ
- iˆ  kˆ = iˆ (correct)
- iˆ  iˆ = 1
- iˆ  ˆj = 0
Given vectors A = 3iˆ + ˆj + 2kˆ and B = 2iˆ − 2 ˆj + 4kˆ, what is the value of A  B?
Given vectors A = 3iˆ + ˆj + 2kˆ and B = 2iˆ − 2 ˆj + 4kˆ, what is the value of A  B?
- 8kˆ - 5jˆ
- 8jˆ - 3kˆ
- 8iˆ + 2jˆ
- 8kˆ + 5iˆ (correct)
If the vectors A and B satisfy A ï‚´ B = 0, what can be inferred about them?
If the vectors A and B satisfy A ï‚´ B = 0, what can be inferred about them?
- They form an angle of exactly 90°
- They are perpendicular to each other
- They are parallel to each other (correct)
- They form an angle less than 90°
Which of these values for λ is meant to be incorrect based on the given conditions?
Which of these values for λ is meant to be incorrect based on the given conditions?
Given the operations on vectors, which one is correct?
Given the operations on vectors, which one is correct?
What is the torque $ au$ when $F = 10 extbf{i} - 10 extbf{j}$ and $r = 5 extbf{i} - 3 extbf{j}$?
What is the torque $ au$ when $F = 10 extbf{i} - 10 extbf{j}$ and $r = 5 extbf{i} - 3 extbf{j}$?
Which of the following is a unit vector perpendicular to the vectors $2 extbf{i} + 3 extbf{j} + extbf{k}$ and $ extbf{i} - extbf{j} + 2 extbf{k}$?
Which of the following is a unit vector perpendicular to the vectors $2 extbf{i} + 3 extbf{j} + extbf{k}$ and $ extbf{i} - extbf{j} + 2 extbf{k}$?
What can be concluded if $A imes B = B imes A$?
What can be concluded if $A imes B = B imes A$?
Which of the following correctly represents the relationship between the magnitude and direction of two perpendicular vectors A and B?
Which of the following correctly represents the relationship between the magnitude and direction of two perpendicular vectors A and B?
What does the cross product of two identical vectors yield?
What does the cross product of two identical vectors yield?
If vectors A and B have a cross product of zero, what can be inferred about their direction?
If vectors A and B have a cross product of zero, what can be inferred about their direction?
What is the result of the expression $A imes A$?
What is the result of the expression $A imes A$?
Which of the following is incorrect when evaluating the cross product of two vectors?
Which of the following is incorrect when evaluating the cross product of two vectors?
Flashcards
Dot product of parallel vectors
Dot product of parallel vectors
The dot product of two parallel vectors is equal to the product of their magnitudes.
Cross product of parallel vectors
Cross product of parallel vectors
The cross product of two vectors is zero if and only if the vectors are parallel.
Dot product of perpendicular vectors
Dot product of perpendicular vectors
The dot product of two perpendicular vectors is zero.
Cross product of perpendicular vectors
Cross product of perpendicular vectors
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Cross product of vectors
Cross product of vectors
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What is torque?
What is torque?
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What is the cross product of two vectors?
What is the cross product of two vectors?
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How do you find the unit vector perpendicular to two vectors?
How do you find the unit vector perpendicular to two vectors?
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What does it mean if the cross product of two vectors is zero?
What does it mean if the cross product of two vectors is zero?
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What is a unit vector?
What is a unit vector?
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Is the cross product of two vectors commutative?
Is the cross product of two vectors commutative?
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What does it mean if the dot product of two vectors is zero?
What does it mean if the dot product of two vectors is zero?
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What does the magnitude of the cross product represent?
What does the magnitude of the cross product represent?
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Study Notes
Vector Operations (NEET 2.0)
- Torque Calculation: Given force vector F = (10î – 10ĵ) and vector r=(5î -3ĵ), calculate torque τ = r × F.
- Unit Vector Perpendicular to Two Vectors: Find the unit vector perpendicular to vectors A and B. Use the formula A × B / |A × B|.
- Perpendicular Vectors: Vectors are perpendicular if their dot product is zero.
Vector Properties (NEET 2.0)
- Vectors Orthogonal to Each Other: Two vectors (2î + 3ĵ + k) and (î – ĵ + 2k) are orthogonal to each other in 3-dimensions. Find a unit vector perpendicular to both vectors.
- Parallel Vectors: If two vectors are antiparallel, their dot product can determine their value.
- Cross Product magnitude: The magnitude of the cross product of vectors A and B is |A × B| = |A||B| sin θ, where θ is the angle between the vectors.
Vector Relationships (NEET 2.0)
- Cross Product Equality: If A × B = B × A, then the angle between vectors A and B is 0 or π.
- Unit Vectors along Axes: i, j, and k are unit vectors along the x, y, and z axes, respectively.
- Cross Product of Unit Vectors: Calculations involve i × j = k, j × k = i, and k × i = j and their reverses
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