Cross Product · Multivariable Calculus

Multivariable Calculus Quiz

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VECTORS AND GEOMETRY IN 3D

Question 1 of 18

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Let

\vec{a}

and

\vec{b}

be vectors in

\mathbb{R}^3

. The parallelogram

P_1

spanned by

\vec{a}

and

\vec{b}

has area

A

. A new parallelogram

P_2

is spanned by the vectors

\vec{u} = 2\vec{a} + \vec{b}

and

\vec{v} = \vec{a} - 3\vec{b}

. What is the area of

P_2

in terms of

A

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