Write the direction ratios of the vector vec{ | vedclass

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(A) The direction ratios of a vector $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$ are the components $(x, y, z)$.For the given vector $\vec{a} = 1\hat{i

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$\left(\frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}}, -\frac{2}{\sqrt{6}}\right)$

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(A) The direction ratios of a vector $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$ are the components $(x, y, z)$.For the given vector $\vec{a} = 1\hat{i} + 1\hat{j} - 2\hat{k}$,the direction ratios are $a = 1, b = 1, c = -2$.Next,we calculate the magnitude of the vector: $|\vec{a}| = \sqrt{1^2 + 1^2 + (-2)^2} = \sqrt{1 + 1 + 4} = \sqrt{6}$.The direction cosines $(l, m, n)$ are given by $l = \frac{a}{|\vec{a}|}, m = \frac{b}{|\vec{a}|}, n = \frac{c}{|\vec{a}|}$.Substituting the values,we get $l = \frac{1}{\sqrt{6}}, m = \frac{1}{\sqrt{6}}, n = \frac{-2}{\sqrt{6}}$.Thus,the direction cosines are $\left(\frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}}, -\frac{2}{\sqrt{6}}\right)$.

Write the direction ratios of the vector $\vec{a} = \hat{i} + \hat{j} - 2\hat{k}$ and hence calculate its direction cosines.

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