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 comp

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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,the values are $x = \frac{36}{5}$ 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 $\vec{B} = (5 \hat{i} + 6 \hat{j} - y \hat{k})$ are parallel are

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