3.13 The scalar product

3.13 The scalar product Quiz

IB Maths: Analysis and Approaches HL: Quiz

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5 questions, one answer each

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  1. 1. Find (3,0,−2)⋅(1,5,4)(3,0,-2)\cdot(1,5,4).

    • A. −5-5
    • B. 1111
    • C. (3,0,−8)(3,0,-8)
    • D. 55

  2. 2. ∣v∣=2|\mathbf{v}|=2, ∣w∣=5|\mathbf{w}|=5 and the angle between them is 120∘120^\circ. Find v⋅w\mathbf{v}\cdot\mathbf{w}.

    • A. 55
    • B. −5-5
    • C. −10-10
    • D. 535\sqrt3

  3. 3. For which kk are (k,2,1)(k,2,1) and (3,−1,4)(3,-1,4) perpendicular?

    • A. −2-2
    • B. 23\frac23
    • C. 22
    • D. −23-\frac23

  4. 4. Which statement is true for all vectors?

    • A. v⋅w=∣v∣∣w∣\mathbf{v}\cdot\mathbf{w}=|\mathbf{v}||\mathbf{w}|
    • B. v⋅v=∣v∣2\mathbf{v}\cdot\mathbf{v}=|\mathbf{v}|^2
    • C. v⋅w=0\mathbf{v}\cdot\mathbf{w}=\mathbf{0} means v=0\mathbf{v}=\mathbf{0}
    • D. (v⋅w)(\mathbf{v}\cdot\mathbf{w}) is a vector

  5. 5. v=(2,−4,6)\mathbf{v}=(2,-4,6) and w=(−1,2,−3)\mathbf{w}=(-1,2,-3). Find ∣v⋅w∣|\mathbf{v}\cdot\mathbf{w}| and decide.

    • A. 2828; parallel
    • B. 00; perpendicular
    • C. 2828; neither
    • D. −28-28; perpendicular

Quiz