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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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Find cos(∠BAD)
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Given that ∠AXD is obtuse, show that cos(∠AXD)=−√215.
Hence find the value of ∣∣∣AC⃗×BD⃗∣∣∣.
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