Vectors

Vectors Quiz

Spec 5.1 · Edexcel IGCSE Maths: Quiz

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5 questions, one answer each

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  1. 1. If a⃗=(2−3)\vec{a} = \begin{pmatrix} 2 \\ -3 \end{pmatrix} and b⃗=(−15)\vec{b} = \begin{pmatrix} -1 \\ 5 \end{pmatrix}, what is a⃗+b⃗\vec{a} + \vec{b}?

    • A. (12)\begin{pmatrix} 1 \\ 2 \end{pmatrix}
    • B. (3−8)\begin{pmatrix} 3 \\ -8 \end{pmatrix}
    • C. (1−2)\begin{pmatrix} 1 \\ -2 \end{pmatrix}
    • D. (−18)\begin{pmatrix} -1 \\ 8 \end{pmatrix}

  2. 2. What is the magnitude of v⃗=(512)\vec{v} = \begin{pmatrix} 5 \\ 12 \end{pmatrix}?

    • A. 17
    • B. 13
    • C. 7
    • D. 60

  3. 3. OA⃗=(31)\vec{OA} = \begin{pmatrix} 3 \\ 1 \end{pmatrix} and OB⃗=(79)\vec{OB} = \begin{pmatrix} 7 \\ 9 \end{pmatrix}. What is AB⃗\vec{AB}?

    • A. (48)\begin{pmatrix} 4 \\ 8 \end{pmatrix}
    • B. (−4−8)\begin{pmatrix} -4 \\ -8 \end{pmatrix}
    • C. (1010)\begin{pmatrix} 10 \\ 10 \end{pmatrix}
    • D. (4−8)\begin{pmatrix} 4 \\ -8 \end{pmatrix}

  4. 4. OA⃗=a⃗\vec{OA} = \vec{a} and OB⃗=b⃗\vec{OB} = \vec{b}. Point MM divides ABAB such that AM:MB=1:3AM:MB = 1:3. What is OM⃗\vec{OM} in terms of a⃗\vec{a} and b⃗\vec{b}?

    • A. 12(a⃗+b⃗)\tfrac{1}{2}(\vec{a}+\vec{b})
    • B. a⃗+14(b⃗−a⃗)\vec{a} + \tfrac{1}{4}(\vec{b}-\vec{a})
    • C. a⃗+34(b⃗−a⃗)\vec{a} + \tfrac{3}{4}(\vec{b}-\vec{a})
    • D. 14a⃗+b⃗\tfrac{1}{4}\vec{a} + \vec{b}

  5. 5. In triangle OABOAB, OA⃗=a⃗\vec{OA} = \vec{a}, OB⃗=b⃗\vec{OB} = \vec{b}. CC is the point such that OC⃗=3a⃗\vec{OC} = 3\vec{a}, and DD is the midpoint of OBOB. Which statement correctly shows AA, and points related to CC and DD, are NOT necessarily collinear just because two vectors are parallel?

    • A. AD⃗\vec{AD} and DC⃗\vec{DC} being scalar multiples always proves AA, DD, CC collinear even without a shared point
    • B. Parallel vectors alone are sufficient to prove collinearity
    • C. Collinearity requires the vectors to be parallel AND to share a common point such as DD
    • D. Collinearity only requires equal magnitudes

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