Find the value of parallelepiped whose edges are represented by a = 2 i - 3 j + 4 k , b = i + 2 j - k , c = 3 i - j + 2 k .

Question

Find the value of parallelepiped whose edges are represented by $\vec{a} = 2 \hat{i} - 3 \hat{j} + 4 \hat{k},$ $\vec{b} = \hat{i} + 2 \hat{j} - \hat{k},$ $\vec{c} = 3 \hat{i} - \hat{j} + 2 \hat{k} .$

Smart Achievers · Accepted Answer

(2)

Ans. 7 cu units

Explanation:

Required volume of parallelepiped $= \vec{a} \cdot (\vec{b} \times \vec{c})$

$\vec{a} \cdot (\vec{b} \times \vec{c}) =$ $| \begin{matrix} 2 & - 3 & 4 \\ 1 & 2 & - 1 \\ 3 & - 1 & 2 \end{matrix} |$

$= 2 (5) + 3 (5) + 4 (- 7)$

$= 10 + 15 - 28 = - 7$

Hence, $| \vec{a} \cdot (\vec{b} \times \vec{c}) |$ $=$ $| - 7 |$

$= 7 cu units$

Solution

Q.
Find the value of parallelepiped whose edges are represented by $\vec{a} = 2 \hat{i} - 3 \hat{j} + 4 \hat{k},$ $\vec{b} = \hat{i} + 2 \hat{j} - \hat{k},$ $\vec{c} = 3 \hat{i} - \hat{j} + 2 \hat{k} .$

1 14 cu units

2 7 cu units

3 8 cu units

4 9 cu units

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