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Consider the three points A=(2,3,4),B=(1,5,3),A=(2,3,4),B=(1,5,3),A=(2,3,4),B=(1,5,3), and C=(2,7,4).C=(2,7,4).C=(2,7,4). What is the area of △ABC?\triangle ABC?△ABC?
Consider a triangle △OAB.\triangle OAB.△OAB. If OA→=(0,2,−2)\overrightarrow{OA}=(0,2,-2)OA=(0,2,−2) and OB→=(1,−4,1),\overrightarrow{OB}=(1,-4,1),OB=(1,−4,1), then what is the area of △OAB?\triangle OAB?△OAB?
If A=(0,1,1),B=(−1,2,3),A=(0,1,1),B=(-1,2,3),A=(0,1,1),B=(−1,2,3), and C=(4,0,−1),C=(4,0,-1),C=(4,0,−1), what is the area of △ABC?\triangle ABC?△ABC?
Consider a parallelogram ABCD.ABCD.ABCD. If A=(−2,3,1),B=(0,5,3),A=(-2,3,1),B=(0,5,3),A=(−2,3,1),B=(0,5,3), and D=(1,7,4),D=(1,7,4),D=(1,7,4), what is the square of the area of ABCD?ABCD?ABCD?
Calculate the area of the triangle spanned by the vectors a⃗ \vec{a}a and b⃗, \vec{b}, b, where ∣a⃗∣=3, \lvert \vec{a} \rvert = 3 ,∣a∣=3, ∣b⃗∣=4 \lvert \vec{b} \rvert = 4 ∣b∣=4 and a⃗⋅b⃗=82. \vec{a} \cdot \vec{b} = 8\sqrt{2}.a⋅b=82.
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