Question:
Direction ratios of the straight line
\[
\vec{r} = 4\hat{i} - 7\hat{j} + 5\hat{k} + s(9\hat{i} - 2\hat{j} + 5\hat{k}) \text{ are:} ........... \]
Direction ratios of the straight line
\[
\vec{r} = 4\hat{i} - 7\hat{j} + 5\hat{k} + s(9\hat{i} - 2\hat{j} + 5\hat{k}) \text{ are:} ........... \]
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The direction ratios of a line are the coefficients of \( \hat{i}, \hat{j}, \) and \( \hat{k} \) in the vector equation of the line.
Updated On: Feb 2, 2026
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Solution and Explanation
Step 1: Understanding direction ratios.
The direction ratios of a line are given by the coefficients of \( \hat{i}, \hat{j}, \) and \( \hat{k} \) in the vector equation of the line. The equation of the line is: \[ \vec{r} = 4\hat{i} - 7\hat{j} + 5\hat{k} + s(9\hat{i} - 2\hat{j} + 5\hat{k}) \] This represents the vector equation of a straight line in 3D space.
Step 2: Identifying the direction ratios.
The direction ratios are the coefficients of \( \hat{i}, \hat{j}, \) and \( \hat{k} \) in the second part of the equation, i.e., the direction ratios are \( 9, -2, 5 \).
Step 3: Conclusion.
Thus, the direction ratios of the straight line are \( 9, -2, 5 \).
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