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CH 1: 1.1 Resultant of perdendicular vectors
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CH 1: 1.1 Resultant of perdendicular vectors

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@GreatestTiger

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Questions and Answers

Which method enables the determination of the magnitude of vectors?

  • Trigonometric methods
  • Algebraic methods (correct)
  • Geometry
  • Calculus

    • What is required to understand the direction of vectors?

  • Calculus
  • Algebraic methods
  • Trigonometric methods
  • Additional considerations (correct)

    • In the example provided, what is the magnitude of the resultant force?

  • 50 N (correct)
  • 20 N
  • 40 N
  • 30 N

    • How does trigonometry help in determining the direction of vectors?

    <p>By employing basic trigonometric principles</p> Signup and view all the answers

    What trigonometric function is specifically mentioned as being used to compute the angle α in the text?

    <p>Tangent function</p> Signup and view all the answers

    What is the angle α, approximately, between the resultant force vector and the positive x-axis?

    <p>36.87 degrees</p> Signup and view all the answers

    How is the resultant force described in the example provided?

    <p>50 N, at a 36.9-degree angle to the x-axis</p> Signup and view all the answers

    What is emphasized in the example regarding determining vector direction?

    <p>Integration of trigonometry</p> Signup and view all the answers

    Which force was acting in the positive x-direction in the given example?

    <p>40 N</p> Signup and view all the answers

    What enables the calculation of the direction of the resultant vector in trigonometry?

    <p>Basic trigonometric principles</p> Signup and view all the answers

    What is essential for understanding the direction of vectors?

    <p>Trigonometric considerations</p> Signup and view all the answers

    In vector analysis, what allows the determination of the magnitude of vectors?

    <p>Algebraic methods</p> Signup and view all the answers

    What is exemplified in Worked Example 11 to determine vector direction?

    <p>Trigonometric principles</p> Signup and view all the answers

    How is the angle α between the resultant force vector and the positive x-axis computed?

    <p>Employing the tangent function</p> Signup and view all the answers

    What type of force was acting concurrently with a force of 40 N in the positive x-direction in the example?

    <p>30 N in the positive y-direction</p> Signup and view all the answers

    What allows for the description of the 50 N resultant force in the example?

    <p>Tangent function calculations</p> Signup and view all the answers

    In vector analysis, what is highlighted by determining the direction of the resultant force?

    <p>Significance of trigonometry</p> Signup and view all the answers

    What becomes feasible in trigonometry concerning vector analysis?

    <p>Direction computation</p> Signup and view all the answers

    What is crucial in determining the angle between the resultant force vector and the positive x-axis?

    <p>Employing trigonometry</p> Signup and view all the answers

    Regarding vector analysis, what does Worked Example 11 emphasize?

    <p>The utilization of trigonometric principles</p> Signup and view all the answers

    How is the magnitude of vectors determined according to the text?

    <p>By employing algebraic methods</p> Signup and view all the answers

    What does the angle α represent in the context of determining the resultant force's direction?

    <p>The angle between the resultant force and the positive x-axis</p> Signup and view all the answers

    How does trigonometry aid in comprehensive vector analysis?

    <p>By helping calculate angles between vectors</p> Signup and view all the answers

    What role does the tangent function play in determining vector direction?

    <p>Computes the angle between vectors</p> Signup and view all the answers

    In vector analysis, what purpose does establishing the direction of the resultant vector serve?

    <p>To enhance the trigonometric principles' application</p> Signup and view all the answers

    Why is understanding the direction of vectors considered to go beyond algebraic methods?

    <p>Due to the need for additional considerations and trigonometric calculations</p> Signup and view all the answers

    What is the significance of determining the angle α in vector analysis?

    <p>It assists in identifying the vector's direction accurately</p> Signup and view all the answers

    What makes Worked Example 11 a significant illustration in the text?

    <p>It exemplifies the application of trigonometry in vector analysis</p> Signup and view all the answers

    Which method does the text emphasize for calculating the direction of the resultant force?

    <p>Trigonometric functions</p> Signup and view all the answers

    What distinguishes the determination of vector direction in vector analysis from solely calculating magnitudes?

    <p>Direction incorporates angles and trigonometry concepts</p> Signup and view all the answers

    What is the angle, in degrees, between the resultant force and the positive y-axis?

    <p>50</p> Signup and view all the answers

    Which trigonometric function is used to calculate the magnitude of vectors in the given example?

    <p>Sine</p> Signup and view all the answers

    What would be the magnitude of the resultant force if a 20 N force acts in the negative x-direction alongside the existing forces?

    <p>30 N</p> Signup and view all the answers

    How would the angle α change if the magnitude of the force in the positive x-direction increased to 50 N while keeping the other force constant?

    <p>Remain constant</p> Signup and view all the answers

    If a force of 30 N acts in the negative y-direction, what is the resultant force's new direction in relation to the positive x-axis?

    <p>90 degrees</p> Signup and view all the answers

    Which mathematical concept plays a significant role in determining the direction of vectors in the provided example?

    <p>Vector multiplication</p> Signup and view all the answers

    If the angle α was incorrectly calculated as 45 degrees instead of 36.87 degrees, what impact would it have on the stated resultant force?

    <p>Increase in magnitude</p> Signup and view all the answers

    What happens to the resultant force's magnitude if both forces in the example act in the negative directions of their respective axes instead of positive directions?

    <p>Magnitude increases</p> Signup and view all the answers

    If a force of 50 N acts in the negative y-direction concurrently with the existing forces, what would be the correct description of the resultant force?

    <p>50 N at 90 degrees to the positive x-axis</p> Signup and view all the answers

    What is the critical difference in approach between determining the magnitude and direction of vectors in the context of trigonometry?

    <p>Magnitude involves scalar calculation, while direction involves vector treatment</p> Signup and view all the answers

    What mathematical concept is instrumental in determining the direction of vectors?

    <p>Trigonometry</p> Signup and view all the answers

    If a force of 60 N in the negative x-direction is introduced alongside the existing forces in the example, what impact would this have on the angle α?

    <p>The angle α will increase</p> Signup and view all the answers

    Which fundamental principle facilitates the determination of the vector's direction in the described example?

    <p>Tangent function</p> Signup and view all the answers

    In the context of the text, what critical consideration does trigonometry introduce when analyzing vectors?

    <p>Direction</p> Signup and view all the answers

    What is the primary significance of the angle α calculated with trigonometric principles in the context of vectors?

    <p>Determining the direction of the resultant vector</p> Signup and view all the answers

    Adding a force of 20 N in the negative y-direction to the existing forces in the example would likely result in:

    <p>Decreasing the resultant force's magnitude</p> Signup and view all the answers

    What does Worked Example 11 emphasize specifically in relation to vector direction analysis?

    <p>Utilizing trigonometric functions</p> Signup and view all the answers

    In the given context, what is the primary limitation of algebraic methods in analyzing vectors?

    <p>Algebraic methods do not yield direction information</p> Signup and view all the answers

    What key aspect distinguishes determining vector direction from calculating vector magnitudes?

    <p>Trigonometric considerations</p> Signup and view all the answers

    If the angle α was misinterpreted as 45 degrees instead of 36.87 degrees, what would this likely lead to?

    <p>An error in stating the direction of the resultant force</p> Signup and view all the answers

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