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  • Perplex
    IB Math AIHL
    /
    Vectors
    /

    Problem Bank

    [Maximum mark: 11]

    The 3D parallelogram ABCD is illustrated in 2D in the diagram below, with ​AB⃗=p​ and ​AD⃗=q. The diagonals ​AC⃗​ and ​BD⃗​ intersect at X. It is given that ​p⋅q=4, ​∣p∣=2, and that ABCD has a perimeter of 10.

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    1. Find ​cos(∠BAD)​

      [3]

      To earn a crown, get your answer ready before you reveal the options!

    2. Given that ​∠AXD​ is obtuse, show that ​cos(∠AXD)=−√215​​.

      [5]
    3. Hence find the value of ​∣∣∣​AC⃗×BD⃗∣∣∣​.

      [3]

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