The vector product of two vectors 2hat{i} + h | vedclass

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Question

(A) The vector product of two vectors $\vec{A} = 2\hat{i} + \hat{j}$ and $\vec{B} = \hat{i} + 2\hat{j}$ is given by the cross product $\vec{A} 	imes

Vedclass · Accepted Answer

$3\hat{k}$

Vedclass · Answer

(A) The vector product of two vectors $\vec{A} = 2\hat{i} + \hat{j}$ and $\vec{B} = \hat{i} + 2\hat{j}$ is given by the cross product $\vec{A} 	imes \vec{B}$.$\vec{A} 	imes \vec{B} = (2\hat{i} + \hat{j}) 	imes (\hat{i} + 2\hat{j})$Using the distributive property of the cross product:$= 2\hat{i} 	imes \hat{i} + 2\hat{i} 	imes 2\hat{j} + \hat{j} 	imes \hat{i} + \hat{j} 	imes 2\hat{j}$Since $\hat{i} 	imes \hat{i} = 0$ and $\hat{j} 	imes \hat{j} = 0$,and knowing $\hat{i} 	imes \hat{j} = \hat{k}$ and $\hat{j} 	imes \hat{i} = -\hat{k}$:$= 0 + 4(\hat{k}) + (-\hat{k}) + 0$$= 3\hat{k}$

The vector product of two vectors $2\hat{i} + \hat{j}$ and $\hat{i} + 2\hat{j}$ is:

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