If the vectors hat{i}+2 hat{j}+x hat{k} and y | vedclass

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(A) Let $\vec{a} = \hat{i} + 2\hat{j} + x\hat{k}$ and $\vec{b} = y\hat{i} + 6\hat{j} + 4\hat{k}$ be two collinear vectors.Since they are collinear,the

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$\frac{4}{3}, 3$

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(A) Let $\vec{a} = \hat{i} + 2\hat{j} + x\hat{k}$ and $\vec{b} = y\hat{i} + 6\hat{j} + 4\hat{k}$ be two collinear vectors.Since they are collinear,there exists a scalar $m$ such that $\vec{a} = m\vec{b}$.Substituting the components,we get: $\hat{i} + 2\hat{j} + x\hat{k} = m(y\hat{i} + 6\hat{j} + 4\hat{k})$.Equating the coefficients of $\hat{i}, \hat{j},$ and $\hat{k}$ on both sides:$1 = my$$2 = 6m \Rightarrow m = \frac{2}{6} = \frac{1}{3}$$x = 4m$Substituting $m = \frac{1}{3}$ into the equations for $x$ and $y$:$x = 4 	imes \frac{1}{3} = \frac{4}{3}$$1 = \frac{1}{3}y \Rightarrow y = 3$Thus,the values are $x = \frac{4}{3}$ and $y = 3$.

If the vectors $\hat{i}+2 \hat{j}+x \hat{k}$ and $y \hat{i}+6 \hat{j}+4 \hat{k}$ are collinear,then the values of $x$ and $y$ are respectively,

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