## Area of Parallelogram Formed By Two Vectors

\[\vec{a} , \: \vec{b}\]

.The area of the parallelogram is the magnitude of the cross or vector product of the vectors

\[\| \vec{a} \times \vec{b} \| = \| \vec{a} \| \| \vec{b} \| sin \theta\]

where \[\theta\]

is the angle between \[\vec{a}\]

and \[\vec{b}\]

.The cross product is itself a vector, perpendicular to both

\[\vec{a}\]

and \[\vec{b}\]

but the area is equal to the magnitude.Then of course, thye area of the triangle formed by

\[\vec{a} , \: \vec{b}\]

is half the area of the parallelogram \[\frac{1}{2} \| \vec{a} \| \| \vec{b} \| sin \theta\]

.