Math Problem Statement
For 𝑣 1 ⃗ v 1
, plot the point (5, 1) and draw the vector from the origin.
Solution
To plot the vector v₁ at the point (5, 1) and draw it from the origin:
- Plot the point (5, 1): Mark the point on the Cartesian plane where the x-coordinate is 5 and the y-coordinate is 1.
- Draw the vector: Start the vector at the origin (0, 0) and draw an arrow pointing towards the point (5, 1). This represents the vector v₁.
The vector will have its tail at the origin (0, 0) and its head at (5, 1). This means the vector has components (5, 1), where 5 is the horizontal (x-axis) component, and 1 is the vertical (y-axis) component.
Would you like me to generate a plot of this vector?
Here are 5 related questions to expand your understanding:
- How can you determine the magnitude of vector v₁?
- What is the direction of vector v₁ in degrees from the positive x-axis?
- How would you plot a vector v₂ = (3, 4) on the same plane?
- What happens if you add two vectors, like v₁ and v₂, graphically?
- Can you express vector v₁ in unit vector form?
Tip: The length of a vector can be found using the Pythagorean theorem, based on its components.
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Math Problem Analysis
Mathematical Concepts
Vectors
Coordinate Geometry
Graphical Representation of Vectors
Formulas
Magnitude of a vector: |v| = √(x² + y²)
Direction of a vector: θ = tan⁻¹(y/x)
Theorems
Pythagorean Theorem
Suitable Grade Level
Grades 9-12
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