vec{A},vec{B},and vec{C} are three non-collin | vedclass

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Question

(A) The vector product $\vec{V} = \vec{B} 	imes \vec{C}$ results in a vector that is perpendicular to the plane containing $\vec{B}$ and $\vec{C}$.Ne

Vedclass · Accepted Answer

It is perpendicular to $\vec{A}$ and lies in the plane of $\vec{B}$ and $\vec{C}$.

Vedclass · Answer

(A) The vector product $\vec{V} = \vec{B} 	imes \vec{C}$ results in a vector that is perpendicular to the plane containing $\vec{B}$ and $\vec{C}$.Next,the vector product $\vec{A} 	imes \vec{V}$ results in a vector that is perpendicular to both $\vec{A}$ and $\vec{V}$.Since $\vec{V}$ is perpendicular to the plane of $\vec{B}$ and $\vec{C}$,any vector perpendicular to $\vec{V}$ must lie within the plane of $\vec{B}$ and $\vec{C}$.Therefore,$\vec{A} 	imes (\vec{B} 	imes \vec{C})$ lies in the plane of $\vec{B}$ and $\vec{C}$ and is perpendicular to $\vec{A}$.

$\vec{A}$,$\vec{B}$,and $\vec{C}$ are three non-collinear,non-coplanar vectors. What can you say about the direction of $\vec{A} \times (\vec{B} \times \vec{C})$?

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