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Q10  Find the area of the parallelogram whose adjacent sides are determined by the vectors   \vec a = \hat i - \hat j + 3 \hat k and \vec b = 2\hat i -7 \hat j + \hat k.

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\vec a = \hat i - \hat j + 3 \hat k

\vec b = 2\hat i -7 \hat j + \hat k

Area of parallelogram with adjescent side \vec a and \vec b,

A=|\vec a\times\vec b|=|(\vec i-\vec j+3\vec k)\times (2\hat i-7\hat j+\hat k)|

A=\begin{vmatrix} \hat i& \hat j & \hat k\\ 1&-1 &3 \\ 2&-7 &1 \end{vmatrix}=|\hat i(-1+21)-\hat j (1-6)+\hat k (-7+2)|

A=|\hat i(20)-\hat j (-5)+\hat k (-5)|=\sqrt{20^2+5^2+(-5)^2}

A=\sqrt{450}=15\sqrt{2}

The area of the parallelogram whose adjacent sides are determined by the vectors   \vec a = \hat i - \hat j + 3 \hat k and \vec b = 2\hat i -7 \hat j + \hat k  is A=\sqrt{450}=15\sqrt{2}

 

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Pankaj Sanodiya

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