Question

Find the area of the parallelogram with adjacent edges a = (1,4,-2) and b = (3, - 1, - 10) by computing [a * b]

Answer 1

Given:-

$a=(1,4,-2),b=(3,-1,-10)$

To find:-

The area of the paralleogram.

So now we simplify,

$a\times b=\begin{bmatrix}{i} & {j} & {k} \\ {1} & {4} & {-2} \\ {3} & {-1} & {-10}\end{bmatrix}$

By furthur simplifying. we get,

$\begin{gathered} \begin{bmatrix}{i} & {j} & {k} \\ {1} & {4} & {-2} \\ {3} & {-1} & {-10}\end{bmatrix}=i(-40-2)-j(-10+6)+k(-1-12) \\ \text{ =-42i+4j-13k} \end{gathered}$

So now,

$\begin{gathered} \lvert a\times b\rvert=\sqrt[]{(-42)^2+4^2+(-13)^2} \\ \text{ =}\sqrt[]{1764+16+169} \\ \text{ =}\sqrt[]{1949} \\ \text{ =44.14} \end{gathered}$

So the area of paralogrgram is 44.14