Vector vec{F_1} is in the direction of the po | vedclass

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(D) The cross product of two vectors $\vec{A}$ and $\vec{B}$ is given by $\vec{A} 	imes \vec{B} = |A||B| \sin(	heta) \hat{n}$.If the cross product i

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$-4\hat{i}$

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(D) The cross product of two vectors $\vec{A}$ and $\vec{B}$ is given by $\vec{A} 	imes \vec{B} = |A||B| \sin(	heta) \hat{n}$.If the cross product is zero,then $\sin(	heta) = 0$,which implies $	heta = 0^\circ$ or $	heta = 180^\circ$.This means the two vectors must be collinear (parallel or anti-parallel).Given $\vec{F_1}$ is in the direction of the positive $X$-axis,$\vec{F_1} = c\hat{i}$ where $c > 0$.For $\vec{F_2}$ to be collinear with $\vec{F_1}$,it must be of the form $k\hat{i}$ for any scalar $k$.Looking at the options,option $D$ is $-4\hat{i}$,which is parallel (anti-parallel) to the $X$-axis.Therefore,the cross product $\vec{F_1} 	imes \vec{F_2} = (c\hat{i}) 	imes (-4\hat{i}) = -4c(\hat{i} 	imes \hat{i}) = 0$.

Vector $\vec{F_1}$ is in the direction of the positive $X$-axis. If its cross product with another vector $\vec{F_2}$ is zero,what could be the vector $\vec{F_2}$?

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