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

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(D) The area of a parallelogram with adjacent sides $\bar{a}$ and $\bar{b}$ is given by $|\bar{a} 	imes \bar{b}| = 20$. We need to find the area of t

Vedclass · Accepted Answer

$140$

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(D) The area of a parallelogram with adjacent sides $\bar{a}$ and $\bar{b}$ is given by $|\bar{a} 	imes \bar{b}| = 20$. We need to find the area of the parallelogram with adjacent sides $(3 \bar{a} + \bar{b})$ and $(2 \bar{a} + 3 \bar{b})$. The area is given by the magnitude of the cross product of these two vectors: $|(3 \bar{a} + \bar{b}) 	imes (2 \bar{a} + 3 \bar{b})|$ $= |3 \bar{a} 	imes 2 \bar{a} + 3 \bar{a} 	imes 3 \bar{b} + \bar{b} 	imes 2 \bar{a} + \bar{b} 	imes 3 \bar{b}|$ 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: $= |0 + 9(\bar{a} 	imes \bar{b}) - 2(\bar{a} 	imes \bar{b}) + 0|$ $= |7(\bar{a} 	imes \bar{b})| = 7 |\bar{a} 	imes \bar{b}|$ Substituting the given value $|\bar{a} 	imes \bar{b}| = 20$: Area $= 7 	imes 20 = 140$ square units.

If the area of the parallelogram with $\bar{a}$ and $\bar{b}$ as two adjacent sides is $20$ square units,then the area of the parallelogram having $3 \bar{a} + \bar{b}$ and $2 \bar{a} + 3 \bar{b}$ as two adjacent sides in square units is

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