Question

Find the area of a parallelogram with adjacent sides u= <4,7, -8> and v= <-2, 5, 11>

Answer 1

Explanation

The area of the parallelogram is

$Area\text{ of a parallelogram =}|\vec{u}\times\vec{v}|$

Using the giving elements of the sides u= <4,7, -8> and v= <-2, 5, 11>, we will have;

$\begin{gathered} \vec{u}\times\vec{v}=\begin{bmatrix}{i} & {j} & {k} \\ {4} & {7} & {-8} \\ {-2} & {5} & {11}\end{bmatrix}=(77-(-40))i-(44-16)j+(20-(-14))k \\ =117i-28j+34k \\ |\vec{u}\times\vec{v}|=\sqrt{117^2+\left(-28\right)^2+\left(34\right)^2}=\sqrt{15629}=125.01599 \\ \end{gathered}$

Answer: 125.016 square units