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Vector Basics
8 Questions
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Vector Basics

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@GodGivenTopaz

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Questions and Answers

In a three-dimensional coordinate system, how many components does a vector have?

  • Four
  • Five
  • Three (correct)
  • Two

    • Which of the following best describes a vector in mathematics?

  • A quantity that has neither magnitude nor direction
  • A quantity that only has direction
  • A quantity that has both magnitude and direction (correct)
  • A quantity that only has magnitude

    • What is the difference between a scalar and a vector?

  • A scalar has only magnitude, while a vector has both magnitude and direction (correct)
  • A scalar has neither magnitude nor direction, while a vector has both magnitude and direction
  • A scalar has both magnitude and direction, while a vector has only magnitude
  • A scalar has only direction, while a vector has both magnitude and direction

    • Which of the following identities is an example of the Binomial Theorem for Positive Integer Indices?

    <p>$a + b^3 = a^3 + 3a^2b + 3ab^2 + b^3$</p> Signup and view all the answers

    What is the expansion of $(a + b)^4$ according to the Binomial Theorem?

    <p>$a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4$</p> Signup and view all the answers

    What is the expansion of $(a + b)^5$ according to the Binomial Theorem?

    <p>$a^5 + 5a^4b + 10a^3b^2 + 10a^2b^3 + 5ab^4 + b^5$</p> Signup and view all the answers

    What is the expansion of $(a + b)^7$ according to the Binomial Theorem?

    <p>$a^7 + 7a^6b + 21a^5b^2 + 35a^4b^3 + 35a^3b^4 + 21a^2b^5 + 7ab^6 + b^7$</p> Signup and view all the answers

    What is the expansion of $(a + b)^6$ according to the Binomial Theorem?

    <p>$a^6 + 6a^5b + 15a^4b^2 + 20a^3b^3 + 15a^2b^4 + 6ab^5 + b^6$</p> Signup and view all the answers

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