Answer:
[tex]8\sqrt{13}[/tex] units
Step-by-step explanation:
We are given that vectors
u=(5,4,6)
v=(1,4,6)
We have to find the are of parallelogram
We know that area of parallelogram with adjacent sides a and b is given by
[tex]\mid a\times b\mid[/tex]
[tex]u=5\hat{i}+4\hat{j}+6\hat{k}[/tex]
[tex]v=\hat{i}+4\hat{j}+6\hat{k}[/tex]
[tex]u\times v=\begin{vmatrix}i&j&k\\5&4&6\\1&4&6\end{vmatrix}[/tex]
[tex]u\times v=-24\hat{j}+16\hat{k}[/tex]
[tex]\mid u\times v\mid=\sqrt{(-24)^2+(16)^2}[/tex]
[tex]\mid u\times v\mid=\sqrt{832}=\sqrt{2\times 2\times 2\times 2\times 2\times 2\times 13}=8\sqrt{13}[/tex]
Therefore, the area of parallelogram=[tex]8\sqrt{13}[/tex] units
