Area of rhombus is ……., where diagonals are $\overrightarrow{\mathbf{a}} = 2\widehat{\dot{\mathbf{i}}} - 3\widehat{\dot{\mathbf{j}}} + 5\widehat{\mathbf{k}}$ and $\overrightarrow{\mathbf{b}} = - \widehat{\dot{\mathbf{i}}} + \widehat{\dot{\mathbf{j}}} + \widehat{\mathbf{k}}$

Question

Dr. Abubacker · Accepted Answer

(c)
$Area\ of\ rhombus = \frac{1}{2}\left| \overrightarrow{\mathbf{a}} 	imes \overrightarrow{\mathbf{b}} ight|$
$= \frac{1}{2}\left| \left( 2\widehat{\dot{\mathbf{i}}} - 3\widehat{\dot{\mathbf{j}}} + 5\widehat{\mathbf{k}} ight) 	imes \left( - \widehat{\dot{\mathbf{i}}} + \widehat{\dot{\mathbf{j}}} + \widehat{\mathbf{k}} ight) ight|$
$= \frac{1}{2}\left| - 8\widehat{\dot{\mathbf{i}}} - 7\widehat{\dot{\mathbf{j}}} - \widehat{\mathbf{k}} ight| = \frac{1}{2}\sqrt{144}$
$= \sqrt{28.5}$

Q. Area of rhombus is ……., where diagonals are $\overrightarrow{\mathbf{a}} = 2\widehat{\dot{\mathbf{i}}} - 3\widehat{\dot{\mathbf{j}}} + 5\widehat{\mathbf{k}}$ and $\overrightarrow{\mathbf{b}} = - \widehat{\dot{\mathbf{i}}} + \widehat{\dot{\mathbf{j}}} + \widehat{\mathbf{k}}$

Explanation

Reviewed by Dr. Abubacker

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