Vectors
30 Questions
0 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the magnitude of the vector a × b?

  • |a||b|cotθ
  • |a||b|tanθ
  • |a||b|cosθ
  • |a||b|sinθ (correct)
  • What is the direction of the vector a × b?

  • Along a
  • Perpendicular to the plane of a and b (correct)
  • Parallel to the plane of a and b
  • Along b
  • If a and b are two vectors, what is the relation between a × b and b × a?

  • a × b = 0.5b × a
  • a × b = 2b × a
  • a × b = -b × a (correct)
  • a × b = b × a
  • If a and b are two vectors, and m is a scalar, what is the relation between ma × b and a × mb?

    <p>ma × b = a × mb</p> Signup and view all the answers

    What is the property of vector product that states a × (b + c) = a × b + a × c?

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

    What is the primary characteristic of a scalar quantity?

    <p>It has only magnitude and no direction</p> Signup and view all the answers

    What is the term used to describe the line of unlimited length of which a vector AB is a segment?

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

    Which of the following is an example of a vector quantity?

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

    What is the magnitude of a vector denoted by?

    <p>| a |</p> Signup and view all the answers

    What is the name of the point from which a vector begins?

    <p>Initial point</p> Signup and view all the answers

    According to the triangle law of vector addition, what does the third side of the triangle represent?

    <p>The sum of the two vectors</p> Signup and view all the answers

    What is the modulus of a vector m a, where a is a non-zero vector and m is a non-zero scalar?

    <p>|m| |a|</p> Signup and view all the answers

    If r = 3i - 4j + 5k, what is the direction cosine of r with respect to the x-axis?

    <p>3/5</p> Signup and view all the answers

    What is the condition for two vectors a and b to be added using the parallelogram law of addition?

    <p>They must be represented by adjacent sides of a parallelogram</p> Signup and view all the answers

    What is the property of vector addition known as, when the order of the vectors being added does not change the result?

    <p>Commutative property</p> Signup and view all the answers

    What is the condition for the vectors a and b to be expressed as linear combinations of three non-coplanar vectors?

    <p>a and b are non-collinear</p> Signup and view all the answers

    What is the result of the vector product (a × b) × (c × d) when a, b, c, and d are vectors?

    <p>a vector</p> Signup and view all the answers

    What is the angle between two planes P1 and P2, determined by the vectors a, b and c, d, respectively, when (a × b) × (c × d) = 0?

    <p>0</p> Signup and view all the answers

    What is the expression for an unknown vector r, when a, b are two known non-collinear vectors?

    <p>r = x a + y b + z (a × b)</p> Signup and view all the answers

    What is the term used to describe the process of finding an unknown vector or a number of vectors satisfying a given condition?

    <p>Solving a vector equation</p> Signup and view all the answers

    What is the number of non-coplanar vectors that can be formed from two known non-collinear vectors a and b?

    <p>3</p> Signup and view all the answers

    What is the condition for two vectors a and b to be parallel?

    <p>a × b = 0</p> Signup and view all the answers

    What is the expression for the vector product of two vectors a and b?

    <p>a × b</p> Signup and view all the answers

    What is the name of the method used to add two vectors a and b, when the third side of the triangle represents the resultant vector?

    <p>Parallelogram law of vector addition</p> Signup and view all the answers

    What is the result of the vector equation (a × b) × (c × d) = 0, when a, b, c, and d are vectors?

    <p>a × b is parallel to c × d</p> Signup and view all the answers

    What is the condition for two vectors a and b to be equal?

    <p>They have the same or parallel support and the same sense.</p> Signup and view all the answers

    What is the reciprocal of a vector?

    <p>A vector having the same direction as the given vector but magnitude equal to the reciprocal of the given vector.</p> Signup and view all the answers

    What is a localized vector?

    <p>A vector which is drawn parallel to a given vector through a specified point in space.</p> Signup and view all the answers

    What is a free vector?

    <p>A vector which is independent of its position in space.</p> Signup and view all the answers

    What is the position vector of a point A?

    <p>The vector OA which represents the position of the point A with respect to a fixed point O.</p> Signup and view all the answers

    More Like This

    Vector Algebra Fundamentals Quiz
    3 questions
    Vector Algebra Essentials Quiz
    11 questions
    Vector Multiplication: Dot and Cross Products
    12 questions
    Cross Product of Vectors
    5 questions
    Use Quizgecko on...
    Browser
    Browser