Question

Find the area of the parallelogram that has the vectors u = (5, 4, 6) and v = (1, 4, 6) as adjacent sides. O 8113 © 2016 832 24

Answer 1

`8√(13)` units

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

`\mid a* b\mid`

`u=5\hat{i}+4\hat{j}+6\hat{k}`

`v=\hat{i}+4\hat{j}+6\hat{k}`

`u* v=\begin{vmatrix}i&j&k\\5&4&6\\1&4&6\end{vmatrix}`

`u* v=-24\hat{j}+16\hat{k}`

`\mid u* v\mid=√((-24)^2+(16)^2)`

`\mid u* v\mid=√(832)=√(2* 2* 2* 2* 2* 2* 13)=8√(13)`

Therefore, the area of parallelogram=
`8√(13)` units