If the vectors 3hat{i} - 2hat{j} + 5hat{k} an | vedclass

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(D) Two vectors $\vec{a} = a_1\hat{i} + a_2\hat{j} + a_3\hat{k}$ and $\vec{b} = b_1\hat{i} + b_2\hat{j} + b_3\hat{k}$ are parallel if their components

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$p = 4/3, q = 10/3$

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(D) Two vectors $\vec{a} = a_1\hat{i} + a_2\hat{j} + a_3\hat{k}$ and $\vec{b} = b_1\hat{i} + b_2\hat{j} + b_3\hat{k}$ are parallel if their components are proportional,i.e.,$\frac{a_1}{b_1} = \frac{a_2}{b_2} = \frac{a_3}{b_3}$.Given vectors are $3\hat{i} - 2\hat{j} + 5\hat{k}$ and $-2\hat{i} + p\hat{j} - q\hat{k}$.Equating the ratios of the components:$\frac{3}{-2} = \frac{-2}{p} = \frac{5}{-q}$.First,solve for $p$:$\frac{3}{-2} = \frac{-2}{p} \Rightarrow 3p = 4 \Rightarrow p = 4/3$.Next,solve for $q$:$\frac{3}{-2} = \frac{5}{-q} \Rightarrow -3q = -10 \Rightarrow q = 10/3$.Thus,$p = 4/3$ and $q = 10/3$.

If the vectors $3\hat{i} - 2\hat{j} + 5\hat{k}$ and $-2\hat{i} + p\hat{j} - q\hat{k}$ are parallel,then find the values of $p$ and $q$.

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