Find the area of the parallelogram that has the given vectors and as adjacent sides.

Question

Find the area of the parallelogram that has the given vectors  and  as adjacent sides.

Quizplus · Accepted Answer

To find the area of the parallelogram, we need to take the cross product of the given vectors:
$$\begin{pmatrix}11 \ ea \ 595\end{pmatrix} 	imes \begin{pmatrix}11 \ ea \ a7\end{pmatrix} = \begin{pmatrix}ae8d \ -5809 \ 0\end{pmatrix}$$
The magnitude of this cross product gives the area of the parallelogram:
$$\left\| \begin{pmatrix}ae8d \ -5809 \ 0\end{pmatrix} ight\| = \sqrt{ae8d^2 + 5809^2} \approx \sqrt{34.6} \approx 5.88$$
Therefore, the closest answer choice is D.

Find the Area of the Parallelogram That Has the Given