Question

What will be the volume of that parallelopiped whose sides are a= i − j + k, b= i − 3j + 4k and c= 2i − 5j + 3k

(a) 5 units

(b) 6 units

(c) 7 units

(d) 8 units

Answer 1

$\begin{array}{l}\text { Volume of parallelopiped }=\left[\begin{array}{lll}\mathbf{a} & \mathbf{b} & \mathbf{c}\end{array}\right]=\left|\begin{array}{lll}1 & -1 & 1 \\1 & -3 & 4 \\2 & -5 & 3\end{array}\right| \\=(-9+20)-(8-3)+(-5+6)=7 \text { units } \\\end{array}$

So, The correct option of this question will be (C).