The values of x and y for which vectors vec{A | vedclass

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(B) Two vectors $\vec{A} = A_x\hat{i} + A_y\hat{j} + A_z\hat{k}$ and $\vec{B} = B_x\hat{i} + B_y\hat{j} + B_z\hat{k}$ are parallel if their components

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$x = -\frac{36}{5}, y = \frac{5}{3}$

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(B) Two vectors $\vec{A} = A_x\hat{i} + A_y\hat{j} + A_z\hat{k}$ and $\vec{B} = B_x\hat{i} + B_y\hat{j} + B_z\hat{k}$ are parallel if their components are proportional,i.e.,$\frac{A_x}{B_x} = \frac{A_y}{B_y} = \frac{A_z}{B_z}$.Given $\vec{A} = 6\hat{i} + x\hat{j} - 2\hat{k}$ and $\vec{B} = 5\hat{i} - 6\hat{j} - y\hat{k}$.Equating the ratios: $\frac{6}{5} = \frac{x}{-6} = \frac{-2}{-y}$.First,solve for $x$: $\frac{6}{5} = \frac{x}{-6} \implies x = \frac{6 	imes (-6)}{5} = -\frac{36}{5}$.Next,solve for $y$: $\frac{6}{5} = \frac{-2}{-y} \implies \frac{6}{5} = \frac{2}{y} \implies 6y = 10 \implies y = \frac{10}{6} = \frac{5}{3}$.Thus,$x = -\frac{36}{5}$ and $y = \frac{5}{3}$.

The values of $x$ and $y$ for which vectors $\vec{A} = (6\hat{i} + x\hat{j} - 2\hat{k})$ and $\vec{B} = (5\hat{i} - 6\hat{j} - y\hat{k})$ may be parallel are

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