For three vectors vec{A}=(-x hat{i}-6 hat{j}- | vedclass

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Question

$\vec{B} 	imes \vec{C}=\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \ -1 & 4 & 3 \ -8 & -1 & 3\end{array}ight|=15

Vedclass · Accepted Answer

$4$

Vedclass · Answer

$\vec{B} 	imes \vec{C}=\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \ -1 & 4 & 3 \ -8 & -1 & 3\end{array}ight|=15 \hat{i}-21 \hat{j}+33 \hat{k}$

$\vec{A} \cdot(\vec{B} 	imes \vec{C})=(-x \hat{i}-6 \hat{j}-2 \hat{k}) \cdot(15 \hat{i}-21 \hat{j}+33 \hat{k})$

$0=-15 x+126-66$

$15 x=60$

$x=4$

For three vectors $\vec{A}=(-x \hat{i}-6 \hat{j}-2 \hat{k})$, $\vec{B}=(-\hat{i}+4 \hat{j}+3 \hat{k})$ and $\vec{C}=(-8 \hat{i}-\hat{j}+3 \hat{k})$, if $\overrightarrow{\mathrm{A}} \cdot(\overrightarrow{\mathrm{B}} \times \overrightarrow{\mathrm{C}})=0$, them value of $\mathrm{x}$ is. . . . . ..

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