Find the scalar and vector products of two vectors. a =(3 i -4 j … - Vidyadip

Question

Find the scalar and vector products of two vectors. $a =(3 \hat{ i }-4 \hat{ j }+5 \hat{ k })$ and $b =(-2 \hat{ i }+\hat{ j }+3 \hat{ k })$

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Answer

$\begin{aligned} a \cdot b & =(3 \hat{ i }-4 \hat{ j }+5 \hat{ k }) \cdot(-2 \hat{ i }+\hat{ j }-3 \hat{ k }) \\ & =-6-4-15 \\ & =-25\end{aligned}$
$
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 }
$

Note $b \times a =-7 \hat{ i }+\hat{ j }+5 \hat{ k }$

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