3.10 Vectors: concepts and algebra

3.10 Vectors: concepts and algebra Quiz

IB Maths: Applications and Interpretation HL: Quiz

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  1. 1. Find the magnitude of 4i−3j+12k4\mathbf{i}-3\mathbf{j}+12\mathbf{k}.

    • A. 55
    • B. 1919
    • C. 1313
    • D. 169169

  2. 2. Find the unit vector in the direction of (34)\begin{pmatrix}3 \\ 4\end{pmatrix}.

    • A. (0.60.8)\begin{pmatrix}0.6 \\ 0.8\end{pmatrix}
    • B. (3747)\begin{pmatrix}\frac37 \\ \frac47\end{pmatrix}
    • C. (1314)\begin{pmatrix}\frac13 \\ \frac14\end{pmatrix}
    • D. (0.120.16)\begin{pmatrix}0.12 \\ 0.16\end{pmatrix}

  3. 3. The vectors (2k−1)\begin{pmatrix}2 \\ k \\ -1\end{pmatrix} and (6−9−3)\begin{pmatrix}6 \\ -9 \\ -3\end{pmatrix} are parallel. Find kk.

    • A. 33
    • B. 99
    • C. −9-9
    • D. −3-3

  4. 4. OA→=(111)\overrightarrow{OA}=\begin{pmatrix}1 \\ 1 \\ 1\end{pmatrix} and OB→=(4513)\overrightarrow{OB}=\begin{pmatrix}4 \\ 5 \\ 13\end{pmatrix}. Find AB→\overrightarrow{AB}.

    • A. (5614)\begin{pmatrix}5 \\ 6 \\ 14\end{pmatrix}
    • B. (3412)\begin{pmatrix}3 \\ 4 \\ 12\end{pmatrix}
    • C. (−3−4−12)\begin{pmatrix}-3 \\ -4 \\ -12\end{pmatrix}
    • D. (3414)\begin{pmatrix}3 \\ 4 \\ 14\end{pmatrix}

  5. 5. A boat travels at 1010 m s−1^{-1} in the direction 3i+4j3\mathbf{i}+4\mathbf{j}. Its velocity is

    • A. 3i+4j3\mathbf{i}+4\mathbf{j}
    • B. 30i+40j30\mathbf{i}+40\mathbf{j}
    • C. 6i+8j6\mathbf{i}+8\mathbf{j}
    • D. 10i+10j10\mathbf{i}+10\mathbf{j}

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