If the vectors (2 hat{imath} - q hat{jmath} + | vedclass

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(A) Two vectors $\vec{a} = a_1 \hat{\imath} + a_2 \hat{\jmath} + a_3 \hat{k}$ and $\vec{b} = b_1 \hat{\imath} + b_2 \hat{\jmath} + b_3 \hat{k}$ are co

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$5/2$

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(A) Two vectors $\vec{a} = a_1 \hat{\imath} + a_2 \hat{\jmath} + a_3 \hat{k}$ and $\vec{b} = b_1 \hat{\imath} + b_2 \hat{\jmath} + b_3 \hat{k}$ are collinear if their corresponding components are proportional,i.e.,$\frac{a_1}{b_1} = \frac{a_2}{b_2} = \frac{a_3}{b_3}$.Given vectors are $(2, -q, 3)$ and $(4, -5, 6)$.Setting the ratios equal,we get:$\frac{2}{4} = \frac{-q}{-5} = \frac{3}{6}$Simplifying the fractions:$\frac{1}{2} = \frac{q}{5} = \frac{1}{2}$From $\frac{1}{2} = \frac{q}{5}$,we find:$q = \frac{5}{2}$

If the vectors $(2 \hat{\imath} - q \hat{\jmath} + 3 \hat{k})$ and $(4 \hat{\imath} - 5 \hat{\jmath} + 6 \hat{k})$ are collinear,then the value of $q$ is

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