Vectors in the Coordinate Plane: Component Form and Magnitude
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Questions and Answers

What is the component form of vector 𝑣 with an initial point 𝑃(0, −7) and a terminal point 𝑄(−9,0)?

  • (−9,7) (correct)
  • (−9, −7)
  • (9,7)
  • (0,0)
  • What is the result of 2𝐮 − 𝐯, expressed as a linear combination of vectors i and j, given 𝐮 = 〈−10,4〉 and 𝐯 = 〈2,3〉?

  • -12𝒊 + 𝒋
  • -2𝒊 - 5𝒋 (correct)
  • -14𝒊 + 𝒋
  • 2𝒊 + 𝒋
  • What is the unit vector with the same direction as 𝐯 = 〈−4, −3〉?

  • < -4√2/7, -3√2/7 >
  • < -4/5, -3/5 > (correct)
  • < 4/5, 3/5 >
  • < -4/5, 3/5 >
  • What is the dot product of vectors 𝑢 =< 5,3 > and 𝑣 =< 12,4 >?

    <p>48</p> Signup and view all the answers

    For two vectors to be orthogonal, the dot product must equal to __________________.

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

    What is the component form and magnitude of vector 𝑃𝑄?

    <p>&lt;5, 2&gt;, 5</p> Signup and view all the answers

    What are the components of the vector 2𝑢 + 3𝑤?

    <p>&lt;8, -7&gt;</p> Signup and view all the answers

    Find a unit vector in the direction of the vector 𝑤 = 5𝑖 + 5𝑗.

    <p>&lt;0.5𝑖 + 0.5𝑗&gt;</p> Signup and view all the answers

    What is the magnitude and direction angle of the vector −3𝑖 − 5𝑗?

    <p>√34, -124.9°</p> Signup and view all the answers

    Given 𝐫 = 5𝐢 − 𝐣, what is the magnitude of 𝐫?

    <p>2√6</p> Signup and view all the answers

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