The vectors overrightarrow{A} and overrightar | vedclass

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(B) Let the plane containing $\overrightarrow{A}$ and $\overrightarrow{B}$ be the $xy$-plane. Thus,$\overrightarrow{A} = A_x \hat{i} + A_y \hat{j}$ an

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cannot be zero

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(B) Let the plane containing $\overrightarrow{A}$ and $\overrightarrow{B}$ be the $xy$-plane. Thus,$\overrightarrow{A} = A_x \hat{i} + A_y \hat{j}$ and $\overrightarrow{B} = B_x \hat{i} + B_y \hat{j}$.Since $\overrightarrow{C}$ lies outside this plane,it must have a non-zero component in the $z$-direction: $\overrightarrow{C} = C_x \hat{i} + C_y \hat{j} + C_z \hat{k}$,where $C_z 
eq 0$.The resultant vector is $\overrightarrow{R} = \overrightarrow{A} + \overrightarrow{B} + \overrightarrow{C} = (A_x + B_x + C_x) \hat{i} + (A_y + B_y + C_y) \hat{j} + C_z \hat{k}$.For the resultant to be zero,all components must be zero. However,the $z$-component is $C_z$,which is given as non-zero.Therefore,the resultant $\overrightarrow{R}$ cannot be zero.

The vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ lie in a plane. Another vector $\overrightarrow{C}$ lies outside this plane. The resultant $\overrightarrow{R} = \overrightarrow{A} + \overrightarrow{B} + \overrightarrow{C}$ of these three vectors:

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