The adjacent sides of a parallelogram are bar | vedclass

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(C) The area of a parallelogram with adjacent sides $\bar{a}$ and $\bar{b}$ is given by the magnitude of their cross product,$|\bar{a} 	imes \bar{b}|

Vedclass · Accepted Answer

$\sqrt{21}$

Vedclass · Answer

(C) The area of a parallelogram with adjacent sides $\bar{a}$ and $\bar{b}$ is given by the magnitude of their cross product,$|\bar{a} 	imes \bar{b}|$.Given $\bar{a} = 0\hat{i} + 1\hat{j} + 2\hat{k}$ and $\bar{b} = 1\hat{i} + 2\hat{j} + 0\hat{k}$.$\bar{a} 	imes \bar{b} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 0 & 1 & 2 \ 1 & 2 & 0 \end{vmatrix}$$= \hat{i}(1 	imes 0 - 2 	imes 2) - \hat{j}(0 	imes 0 - 2 	imes 1) + \hat{k}(0 	imes 2 - 1 	imes 1)$$= \hat{i}(-4) - \hat{j}(-2) + \hat{k}(-1) = -4\hat{i} + 2\hat{j} - \hat{k}$.The area is $|\bar{a} 	imes \bar{b}| = \sqrt{(-4)^2 + (2)^2 + (-1)^2} = \sqrt{16 + 4 + 1} = \sqrt{21}$ square units.

The adjacent sides of a parallelogram are $\bar{a} = \hat{j} + 2\hat{k}$ and $\bar{b} = \hat{i} + 2\hat{j}$. Find its area.

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