If overrightarrow{ F }=2 hat{ i }+hat{ j }-ha | vedclass

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Question

$\overrightarrow{ F }=2 \hat{ i }+\hat{ j }-\hat{ k }$ $\quad \overrightarrow{ r }=3 \hat{ i }+2 \hat{ j }-2 \hat{ k }$

$\overrightarrow{ F } \cdot

Vedclass · Accepted Answer

$10, \sqrt{2}$

Vedclass · Answer

$\overrightarrow{ F }=2 \hat{ i }+\hat{ j }-\hat{ k }$ $\quad \overrightarrow{ r }=3 \hat{ i }+2 \hat{ j }-2 \hat{ k }$

$\overrightarrow{ F } \cdot \overrightarrow{ r }=6+2+2=10$

$\overrightarrow{ F } 	imes \overrightarrow{ r }=\left|\begin{array}{ccc}\hat{ i } & \hat{ j } & \hat{ k } \ 2 & 1 & -1 \ 3 & 2 & -2\end{array}ight|$

$=\hat{ i }(0)-\hat{ j }(-1)+\hat{ k }(1)$

$=\hat{ j }+\hat{ k }$

$|\overrightarrow{ F } 	imes \overrightarrow{ r }|=\sqrt{2}$

If $\overrightarrow{ F }=2 \hat{ i }+\hat{ j }-\hat{ k }$ and $\overrightarrow{ r }=3 \hat{ i }+2 \hat{ j }-2 \hat{ k }$, then the scalar and vector products of $\overrightarrow{ F }$ and $\overrightarrow{ r }$ have the magnitudes respectively as

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