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In this question, distance is measured in feet.
Anna and Michael are flying toy helicopters in straight lines at a constant speeds.
The position of Anna's helicopter, t seconds after it passes through A, is given by
Find the speed of Anna's helicopter.
After 5 seconds, Anna's helicopter passes through point B. Find
the coordinates of B.
the distance ∣∣∣AB⃗∣∣∣
Michael's helicopter travels in the direction ⎝⎛4−12⎠⎞. The two helicopters collide at ⎝⎛aaa⎠⎞, where a∈R.
Find
the value of a.
the position of Michael's helicopter when t=0.
0 / 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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Find cos(∠BAD)
Given that ∠AXD is obtuse, show that cos(∠AXD)=−√215.
Hence find the value of ∣∣∣AC⃗×BD⃗∣∣∣.
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For any two vectors u and v, prove that ∣u×v∣2+(u⋅v)2=∣u∣2∣v∣2.
The obtuse triangle OAB has area 2 and OA⃗⋅OB⃗=−3. Let θ=∠AOB.
Using the identity in part (a), find the value of sin(2θ).
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