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  4. The vector product of two vectors A =2 hat i + hat j - hat k and B =- hat i - hat j +2 hat k is

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Q. The vector product of two vectors $A =2 \hat{ i }+\hat{ j }-\hat{ k }$ and $B =-\hat{ i }-\hat{ j }+2 \hat{ k }$ is

System of Particles and Rotational Motion

Solution:

Given, $A =2 \hat{ i }+\hat{ j }-\hat{ k }, B =-\hat{ i }-\hat{ j }+2 \hat{ k }$
$\therefore$ Vector product, $A \times B =\begin{vmatrix}\hat{ i } & \hat{ j } & \hat{ k } \\ 2 & 1 & -1 \\ -1 & -1 & 2\end{vmatrix}$
$=\hat{ i }(2-1)-\hat{ j }(4-1)+\hat{ k }(-2+1)=\hat{ i }-3 \hat{ j }-\hat{ k }$