Vectors

Flashcard
•
Mathematics
•
11th - 12th Grade
•
Hard
+1
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15 questions
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1.
FLASHCARD QUESTION
Front
What are the vertical and horizontal components of a vector?
Back
The vertical and horizontal components of a vector can be found using trigonometric functions. For a vector represented as \( \mathbf{v} = \langle x, y \rangle \), the horizontal component is \( x \) and the vertical component is \( y \).
Tags
CCSS.HSN.VM.A.2
2.
FLASHCARD QUESTION
Front
How do you add two vectors?
Back
To add two vectors \( \mathbf{u} = \langle u_1, u_2 \rangle \) and \( \mathbf{v} = \langle v_1, v_2 \rangle \), you add their corresponding components: \( \mathbf{u} + \mathbf{v} = \langle u_1 + v_1, u_2 + v_2 \rangle \).
Tags
CCSS.HSN-VM.B.4A
CCSS.HSN-VM.B.4B
3.
FLASHCARD QUESTION
Front
What is the formula to find the direction angle of a vector?
Back
The direction angle \( \theta \) of a vector \( \mathbf{v} = \langle x, y \rangle \) can be found using the formula: \( \theta = \tan^{-1}\left(\frac{y}{x}\right) \).
Tags
CCSS.HSN.VM.A.1
4.
FLASHCARD QUESTION
Front
What is the significance of the angle in vector representation?
Back
The angle of a vector indicates its direction in the coordinate system. It helps in understanding how the vector is oriented relative to the axes.
Tags
CCSS.HSN.VM.A.1
5.
FLASHCARD QUESTION
Front
What is the relationship between the components of a vector and its magnitude?
Back
The magnitude \( ||\mathbf{v}|| \) of a vector \( \mathbf{v} = \langle x, y \rangle \) is given by the formula: \( ||\mathbf{v}|| = \sqrt{x^2 + y^2} \).
Tags
CCSS.HSN.VM.A.1
6.
FLASHCARD QUESTION
Front
How do you determine if two vectors are equal?
Back
Two vectors \( \mathbf{u} = \langle u_1, u_2 \rangle \) and \( \mathbf{v} = \langle v_1, v_2 \rangle \) are equal if and only if their corresponding components are equal: \( u_1 = v_1 \) and \( u_2 = v_2 \).
Tags
CCSS.HSN.VM.A.1
7.
FLASHCARD QUESTION
Front
What is a unit vector?
Back
A unit vector is a vector that has a magnitude of 1. It is often used to indicate direction. A unit vector in the direction of vector \( \mathbf{v} \) is given by \( \hat{v} = \frac{\mathbf{v}}{||\mathbf{v}||} \).
Tags
CCSS.HSN.VM.A.1
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