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  • Perplex
    IB Math AIHL
    /
    Vectors
    /

    Problems

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    Problem Bank - Vectors

    Access custom-built, exam-style problems for vectors. Each problem has a full solution and mark-scheme, as well as AI grading and support.

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    IB: 4
    1

    0 / 5

    The unit vector b^=⎝⎛​p0q​⎠⎞​ is perpendicular to a=⎝⎛​132​⎠⎞​. Find the possible values of p and q.

    [5]
    2

    0 / 5

    Find a unit vector perpendicular to the vectors i+2j+2k and 2i+j−2k.

    [5]
    3

    0 / 5

    Points A and B have coordinates (1,2,−1) and (3,−4,m), respectively.

    1. Express the displacement vector AB⃗ in terms of m.

      [2]

    It is given that ∣∣∣​AB⃗∣∣∣​=7.

    1. Find the possible values of m.

      [3]
    4

    0 / 7

    Consider the lines with vector equations

    r1​=⎝⎛​1−2a−3​⎠⎞​+λ⎝⎛​a−2a3​⎠⎞​r2​=⎝⎛​a+251​⎠⎞​+μ⎝⎛​a+92−2​⎠⎞​

    where a∈R.

    1. Given that the lines are perpendicular, Find the possible value(s) for a.

      [3]

    Now consider the case where a>0.

    1. Determine with justification whether the lines are parallel, intersecting or skew.

      [4]
    5
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