Find the area of the parallelogram that has the vectors as adjacent sides.
$$\mathbf { u } = \langle 4 , - 1,4 \rangle , \mathbf { v } = \langle 2 , - 3,0 \rangle$$
A) 11
B) $\sqrt { 77 }$
C) $\sqrt { 11 }$
D) 4
E) $2 \sqrt { 77 }$

Question

Quizplus · Accepted Answer

The area of a parallelogram with adjacent sides given by vectors $\mathbf{u}$ and $\mathbf{v}$ is the magnitude of their cross product. The cross product $\mathbf{u} \times \mathbf{v}$ is $\langle 12, 8, -10 \rangle$, and its magnitude is $\sqrt{12^2 + 8^2 + (-10)^2} = \sqrt{144 + 64 + 100} = \sqrt{308} = 2\sqrt{77}$.

Find the Area of the Parallelogram That Has the Vectors u=⟨4,−1,4⟩,v=⟨2,−3,0⟩\mathbf { u } = \langle 4 , - 1,4 \rangle , \mathbf { v } = \langle 2 , - 3,0 \rangleu=⟨4,−1,4⟩,v=⟨2,−3,0⟩

Find the Area of the Parallelogram That Has the Vectors $\mathbf { u } = \langle 4 , - 1,4 \rangle , \mathbf { v } = \langle 2 , - 3,0 \rangle$