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:

  1. Plot the point (5, 1): Mark the point on the Cartesian plane where the x-coordinate is 5 and the y-coordinate is 1.
  2. 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:

  1. How can you determine the magnitude of vector v₁?
  2. What is the direction of vector v₁ in degrees from the positive x-axis?
  3. How would you plot a vector v₂ = (3, 4) on the same plane?
  4. What happens if you add two vectors, like v₁ and v₂, graphically?
  5. 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.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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