Given: vec{A} = 2hat{i} + phat{j} + qhat{k} a | vedclass

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(A) 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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$\frac{14}{5}$ and $\frac{6}{5}$

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(A) 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 $\vec{A} = 2\hat{i} + p\hat{j} + q\hat{k}$ and $\vec{B} = 5\hat{i} + 7\hat{j} + 3\hat{k}$.Equating the ratios of the components: $\frac{2}{5} = \frac{p}{7} = \frac{q}{3}$.For $p$: $\frac{2}{5} = \frac{p}{7} \Rightarrow p = \frac{2 	imes 7}{5} = \frac{14}{5}$.For $q$: $\frac{2}{5} = \frac{q}{3} \Rightarrow q = \frac{2 	imes 3}{5} = \frac{6}{5}$.Thus,the values are $p = \frac{14}{5}$ and $q = \frac{6}{5}$.

Given: $\vec{A} = 2\hat{i} + p\hat{j} + q\hat{k}$ and $\vec{B} = 5\hat{i} + 7\hat{j} + 3\hat{k}$. If $\vec{A} \parallel \vec{B}$,then the values of $p$ and $q$ are,respectively:

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