Find the area of the parallelogram that has the vectors as adjacent sides.
$$\mathbf { u } = \langle 2,3,5 \rangle , \mathbf { v } = \langle - 3,3 , - 5 \rangle$$
A) 3
B) $\sqrt { 46 }$
C) $\sqrt { 22 }$
D) 34
E) $5 \sqrt { 46 }$

Question

Quizplus · Accepted Answer

The area of the parallelogram formed by vectors $\mathbf{u}$ and $\mathbf{v}$ is given by the magnitude of their cross product. The cross product $\mathbf{u} \times \mathbf{v}$ is $\langle -30, -5, 15 \rangle$, and its magnitude is $\sqrt{(-30)^2 + (-5)^2 + 15^2} = 5\sqrt{46}$.

Find the Area of the Parallelogram That Has the Vectors u=⟨2,3,5⟩,v=⟨−3,3,−5⟩\mathbf { u } = \langle 2,3,5 \rangle , \mathbf { v } = \langle - 3,3 , - 5 \rangleu=⟨2,3,5⟩,v=⟨−3,3,−5⟩

Find the Area of the Parallelogram That Has the Vectors $\mathbf { u } = \langle 2,3,5 \rangle , \mathbf { v } = \langle - 3,3 , - 5 \rangle$