Question

Find the volume of the parallelopiped, if the coterminous edges are given by the vectors 2$\hat{i}$ +5$\hat{j}$ -4$\hat{k}$ , 5$\hat{i}$ +7$\hat{j}$ +5$\hat{k}$ , 4$\hat{i}$ + 5$\hat{j}$ - 2$\hat{k}$

Answer 1

Answer:

volume of parallelopiped = 84 cube-unit

Step-by-step explanation:

To find the volume of parallelopiped ,with coterminous edges are given by the vectors,we must calculate Scalar Triplet of the given vectors

Volume of parallelopiped = $[\vec{a}\:\:\:\vec{b}\:\:\:\vec{c}]$

if$\vec{a}=2\hat{i} +5\hat{j} -4\hat{k}\\\\\vec{b}=5\hat{i} +7\hat{j} +5\hat{k}\\\\\vec{c}=4\hat{i} + 5\hat{j} - 2\hat{k}$

$[\vec{a}\:\:\:\vec{b}\:\:\:\vec{c}]$

=$\left|\begin{array}{ccc}2&5&-4\\5&7&5\\4&5&-2\end{array}\right|\\ \\\\=|2(-14-25)-5(-10-20)-4(25-28)|\\\\\\=|-78+150+12|\\\\\\84 unit^{3}$