If the area of the parallelogram with bar{a} | vedclass

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(C) The area of a parallelogram with adjacent sides $\bar{a}$ and $\bar{b}$ is given by $|\bar{a} 	imes \bar{b}|$. Given that $|\bar{a} 	imes \bar{b

Vedclass · Accepted Answer

$105$

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(C) The area of a parallelogram with adjacent sides $\bar{a}$ and $\bar{b}$ is given by $|\bar{a} 	imes \bar{b}|$. Given that $|\bar{a} 	imes \bar{b}| = 15$. The area of the new parallelogram with adjacent sides $(3 \bar{a} + 2 \bar{b})$ and $(\bar{a} + 3 \bar{b})$ is given by the magnitude of their cross product: $|(3 \bar{a} + 2 \bar{b}) 	imes (\bar{a} + 3 \bar{b})|$ $= |3(\bar{a} 	imes \bar{a}) + 9(\bar{a} 	imes \bar{b}) + 2(\bar{b} 	imes \bar{a}) + 6(\bar{b} 	imes \bar{b})|$ Since $\bar{a} 	imes \bar{a} = 0$ and $\bar{b} 	imes \bar{b} = 0$,and $\bar{b} 	imes \bar{a} = -(\bar{a} 	imes \bar{b})$,we have: $= |0 + 9(\bar{a} 	imes \bar{b}) - 2(\bar{a} 	imes \bar{b}) + 0|$ $= |7(\bar{a} 	imes \bar{b})| = 7 |\bar{a} 	imes \bar{b}|$ $= 7 	imes 15 = 105$ square units.

If the area of the parallelogram with $\bar{a}$ and $\bar{b}$ as two adjacent sides is $15$ square units,then the area (in square units) of the parallelogram,having $3 \bar{a} + 2 \bar{b}$ and $\bar{a} + 3 \bar{b}$ as two adjacent sides,is

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