Find the scalar and vector products of two vectors. $a =(3 \hat{ i }-4 \hat{ j }+5 \hat{ k })$ and $b =(- 2 \hat{ i }+\hat{ j }- 3 \hat { k } )$
Find the scalar and vector products of two vectors. $a =(3 \hat{ i }-4 \hat{ j }+5 \hat{ k })$ and $b =(- 2 \hat{ i }+\hat{ j }- 3 \hat { k } )$
$\begin{aligned} a \cdot b &=(3 \hat{ i }-4 \hat{ j }+5 \hat{ k }) \cdot(-2 \hat{ i }+\hat{ j }-3 \hat{ k }) \\ &=-6-4-15 \\ &=-25 \end{aligned}$
$a \times b =\left|\begin{array}{ccc}\hat{ i } & \hat{ j } & \hat{ k } \\ 3 & -4 & 5 \\ -2 & 1 & -3\end{array}\right|=7 \hat{ i }-\hat{ j }-5 \hat{ k }$
$b \times a =-7 \hat{ i }+\hat{ j }+5 \hat{ k }$
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