Find the area of the parallelogram that has the vectors as adjacent sides. $\mathbf { u } = ( 3 ) \mathbf { i } + ( 3 ) \mathbf { j } + ( - 4 ) \mathbf { k } , \quad \mathbf { v } = ( - 4 ) \mathbf { i } + ( 5 ) \mathbf { j } + ( 1 ) \mathbf { k }$
A)3 square units
B) $0$ square units
C) $1$ square units
D)37 square units
E) $\sqrt { 1427 }$ square units

Question

Find the area of the parallelogram that has the vectors as adjacent sides.  $\mathbf { u } = ( 3 ) \mathbf { i } + ( 3 ) \mathbf { j } + ( - 4 ) \mathbf { k } , \quad \mathbf { v } = ( - 4 ) \mathbf { i } + ( 5 ) \mathbf { j } + ( 1 ) \mathbf { k }$
A)3 square units
B) $0$ square units
C) $1$ square units
D)37 square units
E) $\sqrt { 1427 }$ square units

Quizplus · Accepted Answer

The area of the parallelogram is given by the magnitude of the cross product of the vectors $\mathbf{u}$ and $\mathbf{v}$. The cross product $\mathbf{u} \times \mathbf{v}$ is $(-19)\mathbf{i} + (13)\mathbf{j} + (27)\mathbf{k}$. The magnitude is $\sqrt{(-19)^2 + 13^2 + 27^2} = \sqrt{1427}$.

Find the Area of the Parallelogram That Has the Vectors