High School
SAT
ACT
University
MCAT
LSAT
DAT

Practice Question: Application of Cross Product

Related Topics

Wize University Linear Algebra Textbook > Products of Vectors

Cross Product and Area

3 Activities

checklist
Mark Yourself Question
  1. Grab a piece of paper and try this problem yourself.
  2. When you're done, check the "I have answered this question" box below.
  3. View the solution and report whether you got it right or wrong.

Practice Question: Application of Cross Product

Find the area of the triangle that has edges defined by 𝑢⃗=(−1,0,2)𝑢⃗ = (−1,0,2) and 𝑣=(3,−3,0)𝑣=(3,−3,0)


More Cross Product and Area Questions:
Practice: Cross Product and Areas
Find the area of the triangle with vertices M(−3,−1,0)M(-3,-1,0), N(3,1,−1)N(3,1,-1), and P(−2,−1,0)P(-2,-1,0)
133 - FML 3 - 18.1W e.g. 28
Find the area of the parallelogram with vertices at (2,−3), (0,2), (13,−14),\bcb{(2,-3),~(0,2),~(13,-14),} and (11,−9)\bcb{(11,-9)}.
133 - FML 3 - 18.1W e.g. 27
Find the area of the triangle defined by the vectors [57]\bcb{\boldsymbol{ \begin{bmatrix} 5 \\ 7 \end{bmatrix}}} and [31]\bcb{\boldsymbol{ \begin{bmatrix} 3 \\ 1 \end{bmatrix}}}.
133 - FML 3 - 18.1W e.g. 39.1
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 area of the triangle with vertices P1, P2, P3\bcb{P_1,\, P_2,\, P_3}.
Practice: Cross Product (2)
Let X=(0, 0, 0), Y=(1, 1, 0), & Z=(0, 1, 1).X=(0,~0,~0),~Y=(1,~1,~0),~\&~Z=(0,~1,~1)..
What is the area of the triangle XYZ?
$\tkct{cut from 19.4F}$ Mid $\tkco{ S}$ | 133 - FML 3 - 18.1W e.g. 39.1_$\tkcth{Mock F}\tkct{?}$_$\tkct{no vid / soln }$
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 area of the triangle with vertices P1, P2, P3\bcb{P_1,\, P_2,\, P_3}.
A parallelogram in R3R^3 has vertices A(−1,1,2)A\left(-1,1,2\right), B(1,−2,8)B\left(1,-2,8\right) and C=(3,−1,2)C=\left(3,-1,2\right).
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 area of the parallelogram defined by the vectors u→=(1,3,0)\overrightarrow{u}=\left(1,3,0\right)and v→=(−2,0,1)\overrightarrow{v}=\left(-2,0,1\right).
Cross Product and Area
Find the area of the parallelogram ABCD that has vertices A(1,2,5)A(1,2,5), B(−3,0,2)B(-3,0,2), C(−3,−5,−2)C(-3,-5,-2) and D(1,−3,1)D(1,-3,1).