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133 - FML 3 - 18.1W e.g. 39.2

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Wize University Linear Algebra Textbook > Products of Vectors

Volume of a Parallelepiped (Triple Product)

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Consider the points P1=(1,4,1)\bcb{P_1 = (1,4,1)}, P2=(3,4,−1)\bcb{P_2 = (3,4,-1)}, P3=(2,4,−2)\bcb{P_3 = (2,4,-2)}, P4=(0,2,0)\bcb{P_4 = (0,2,0)}.
Find the volume of the parallelepiped defined by the vectors P1P2⃗\bcb{\vec{P_1P_2}}, P1P3⃗\bcb{\vec{P_1P_3}} and P1P4⃗\bcb{\vec{P_1P_4}}.


More Volume of a Parallelepiped (Triple Product) Questions:
Practice Question: Cross Product and Volume
Practice Question: Application of Cross Product
Find the volume of the parallelepiped defined by the vectors u⃗=(1,2,0), v⃗=(0,3,1)\vec{u}=\left(1,2,0\right),\ \vec{v}=\left(0,3,1\right) and w⃗=(1,1,5)\vec{w}=\left(1,1,5\right).
$\tkct{cut from 19.4F}$ Mid $\tkco{ S}$ | 133 - FML 3 - 18.1W e.g. 39.2_$\tkcth{Mock F}\tkct{?}$_$\tkct{no soln / vid}$
Consider the points P1=(1,4,1)\bcb{P_1 = (1,4,1)}, P2=(3,4,−1)\bcb{P_2 = (3,4,-1)}, P3=(2,4,−2)\bcb{P_3 = (2,4,-2)}, P4=(0,2,0)\bcb{P_4 = (0,2,0)}.
Find the volume of the parallelepiped defined by the vectors P1P2⃗\bcb{\vec{P_1P_2}}, P1P3⃗\bcb{\vec{P_1P_3}} and P1P4⃗\bcb{\vec{P_1P_4}}.
Practice Question: Cross Product and Volume
Practice Question: Application of Cross Product
Find the volume of the parallelepiped defined by the vectors u⃗=(1,2,0), v⃗=(0,3,1)\vec{u}=\left(1,2,0\right),\ \vec{v}=\left(0,3,1\right) and w⃗=(1,1,5)\vec{w}=\left(1,1,5\right).
Find the volume of the parallelepiped determined by 𝑢⃗=(1,3,3),𝑣⃗=(1,0,2),𝑢⃗ = (1,3,3), \vec𝑣 = (1,0,2), and 𝑤⃗=(0,2,3). 𝑤⃗= (0,2,3).
Additional practice problems--vector products
Additional Practice Problems--Vector Products
1. If u⃗=(−2,3,−1),  v⃗=(−1,−2,3)\vec{u}=\left(-2,3,-1\right),\ \ \vec{v}=\left(-1,-2,3\right), find
a) u⃗ ∙ v⃗\vec{u}\ \bullet\ \vec{v}
Find the volume of the parallelepiped defined by the vectors u→=(1,0,1)\overrightarrow{u}=\left(1,0,1\right), v→=(2,−1,0)\overrightarrow{v}=\left(2,-1,0\right)and w→=(3,−3,4)\overrightarrow{w}=\left(3,-3,4\right).