Two vectors overrightarrow{A} and overrightar | vedclass

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Question

(B) Let the plane containing $\overrightarrow{A}$ and $\overrightarrow{B}$ be the $xy$-plane. Thus,$\overrightarrow{A} + \overrightarrow{B}$ also lies

Vedclass · Accepted Answer

Cannot be zero

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(B) Let the plane containing $\overrightarrow{A}$ and $\overrightarrow{B}$ be the $xy$-plane. Thus,$\overrightarrow{A} + \overrightarrow{B}$ also lies in the $xy$-plane.Since $\overrightarrow{C}$ lies outside this plane,it must have a non-zero component perpendicular to the $xy$-plane (i.e.,along the $z$-axis).Let $\overrightarrow{R} = \overrightarrow{A} + \overrightarrow{B} + \overrightarrow{C}$.For the resultant $\overrightarrow{R}$ to be zero,the sum of the components along the $z$-axis must be zero.Since $\overrightarrow{A}$ and $\overrightarrow{B}$ have zero components along the $z$-axis,the $z$-component of the resultant is equal to the $z$-component of $\overrightarrow{C}$.Because $\overrightarrow{C}$ is outside the plane,its $z$-component is non-zero,so the resultant $\overrightarrow{R}$ cannot be zero.

Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ lie in a plane,and another vector $\overrightarrow{C}$ lies outside this plane. Then,the resultant of these three vectors,i.e.,$\overrightarrow{A} + \overrightarrow{B} + \overrightarrow{C}$:

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