(vec{a}-vec{b}) times(vec{a}+vec{b}) is equal | vedclass

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(C) Using the distributive property of the cross product:$(\vec{a}-\vec{b}) 	imes(\vec{a}+\vec{b}) = \vec{a} 	imes \vec{a} + \vec{a} 	imes \vec{b}

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$2(\vec{a} 	imes \vec{b})$

Vedclass · Answer

(C) Using the distributive property of the cross product:$(\vec{a}-\vec{b}) 	imes(\vec{a}+\vec{b}) = \vec{a} 	imes \vec{a} + \vec{a} 	imes \vec{b} - \vec{b} 	imes \vec{a} - \vec{b} 	imes \vec{b}$Since the cross product of any vector with itself is zero,$\vec{a} 	imes \vec{a} = 0$ and $\vec{b} 	imes \vec{b} = 0$.Also,using the anticommutative property,$-\vec{b} 	imes \vec{a} = \vec{a} 	imes \vec{b}$.Therefore,the expression becomes $0 + \vec{a} 	imes \vec{b} + \vec{a} 	imes \vec{b} - 0 = 2(\vec{a} 	imes \vec{b})$.

$(\vec{a}-\vec{b}) \times(\vec{a}+\vec{b})$ is equal to :

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