Find the volume of the parallelopiped whose coterminous edges are represented by $a = 2 i - 3 j + 4 k, b = i + 2 j - k, c = 3 i - j + 2 k$

Open in App

Solution

Volume $= ∣ ∣ ∣ ∣ \begin{matrix} 2 & - 3 & 4 1 & 2 & - 1 3 & - 1 & 2 \end{matrix} ∣ ∣ ∣ ∣$
$= 2 (4 - 1) + 3 (2 + 3) + 4 (- 1 - 6)$
$= 6 + 15 - 28 = | - 7 | = 7$

Suggest Corrections

Similar questions

\vec{a} = 2 \hat{i} + 3 \hat{j} + 4 \hat{k}, \vec{b} = \hat{i} + 2 \hat{j} - \hat{k}, \vec{c} = 3 \hat{i} - \hat{j} + 2 \hat{k}

\vec{a} = 2 \hat{i} - 3 \hat{j} + 4 \hat{k}, \vec{b} = \hat{i} + 2 \hat{j} - \hat{k}, \vec{c} = 3 \hat{i} - \hat{j} - 2 \hat{k}

\vec{a} = 11 \hat{i}, \vec{b} = 2 \hat{j}, \vec{c} = 13 \hat{k}

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

¯ ¯ ¯ a = 3 ¯ i - ¯ j + 4 ¯ ¯ ¯ k, ¯ ¯ b = 2 ¯ i + 3 ¯ j - ¯ ¯ ¯ k

¯ ¯ c = - 5 ¯ i + 2 ¯ j + 3 ¯ ¯ ¯ k

¯ ¯ ¯ p = ¯ i + ¯ j + 3 ¯ ¯ ¯ k, ¯ ¯ ¯ q = ¯ i - 2 ¯ j + λ ¯ ¯ ¯ k

¯ ¯ ¯ r = 2 ¯ i + 3 ¯ j

λ

O A = 2 i - 3 j,

O B = i + j - k, O C = 3 i - k

^i -^j +^k, 2^i - 4^j + 5^k,^3 i - 5^j + 2^k

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

\vec{a} = 2 \hat{i} - 3 \hat{j}, \vec{b} = \hat{i} + \hat{j} - \hat{k} and \vec{c} = 3 \hat{i} - \hat{k}

\vec{a} = \hat{i} - 2 \hat{j} + 3 \hat{k}, \vec{b} = 2 \hat{i} + \hat{j} - \hat{k} and \vec{c} = \hat{j} + \hat{k}

\vec{a} = 2 \hat{i} + 3 \hat{j} + \hat{k}, \vec{b} = \hat{i} - 2 \hat{j} + \hat{k} and \vec{c} = - 3 \hat{i} + \hat{j} + 2 \hat{k}

Join BYJU'S Learning Program