Math Problem Statement
Review the graph.
On a coordinate plane, vector u has origin (negative 2, 3) and terminal point (6, 3).
What are the characteristics of the vector shown?
magnitude of 8 and direction angle equal to 0° magnitude of 8 and direction angle equal to 180° magnitude of 2 StartRoot 2 EndRoot and direction angle equal to 0° magnitude of 2 StartRoot 2 EndRoot and direction angle equal to 180°
Solution
To analyze the vector , we’ll calculate its characteristics using its origin and terminal points.
Step 1: Determine the Vector Components
The vector has an origin at and a terminal point at . The components of can be calculated as:
Step 2: Calculate the Magnitude
The magnitude of is given by:
Step 3: Determine the Direction Angle
Since the vector lies on the x-axis and moves to the right (positive x-direction), its direction angle is .
Conclusion
The vector has:
- Magnitude of 8
- Direction angle of
Answer
The correct option is: Magnitude of 8 and direction angle equal to
Would you like further clarification on any steps?
Here are some related questions to extend understanding:
- How would the vector’s direction angle change if it pointed left instead of right?
- What would the magnitude be if the vector spanned from (6, 3) to (-2, 3)?
- How can we find a unit vector with the same direction as ?
- How does the magnitude change if the vector's components double?
- What would the direction angle be for a vector lying on the y-axis?
Tip: A vector lying entirely on the x-axis has a direction angle of if it points to the right and if it points to the left.
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Math Problem Analysis
Mathematical Concepts
Vectors
Coordinate Geometry
Magnitude and Direction of a Vector
Formulas
Vector components formula: (x2 - x1, y2 - y1)
Magnitude formula: |u| = √((x2 - x1)^2 + (y2 - y1)^2)
Direction angle for horizontal vectors
Theorems
-
Suitable Grade Level
Grades 9-10
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