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홈 / 라이브러리 / JEE Main Master Class: Calculus, Mechanics, Coordinate Geometry / AI 플래시카드

How is vector cross product $\vec{a} \times \vec{b}$ computed using components?

덱 'JEE Main Master Class: Calculus, Mechanics, Coordinate Geometry'의 플래시카드.

정답

$\vec{a} \times \vec{b} = \det \begin{pmatrix} \hat{i} & \hat{j} & \hat{k} \\ a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \end{pmatrix}$, resulting in a vector perpendicular to both $\vec{a}$ and $\vec{b}$.

해설

Magnitude is $|\vec{a} \times \vec{b}| = |\vec{a}||\vec{b}|\sin\theta$, representing the area of the parallelogram formed by the vectors.

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