Question

find the volume of parallelopiped with coterminal edges I+j, j+k, k+i​

Answer 1

Step-by-step explanation:

Volume of parallelopiped = 5 unit cube

Step-by-step explanation:

To find the volume of the parallelepiped having coterminous edges

\vec a = \hat i+\hat j+\hat k\\ \\\vec b = \hat i-\hat j\\\\\vec c = \hat i+2\hat j-\hat k\\\\

we have to calculate Scalar triplet

[\vec a\:\:\:\vec b\:\:\:\vec c]=\vec a.(\vec b\times \vec c)\\\\for\\\\(\vec b\times \vec c)=\left|\begin{array}{ccc}\hat i&\hat j&\hat k\\1&-1&0\\1&2&-1\end{array}\right| \\\\=\hat i (1-0)-\hat j (-1-0)+\hat k (2+1)\\\\=\hat i+\hat j+3\:\hat k\\\\\\

\vec a.(\vec b \times \vec c)=(\hat i+\hat j+\hat k).((\hat i+\hat j+3\hat k)\\\\=1+1+3\\\\= 5\:\:unit\:\:cube