Straight line in space — Maths STD 12 Science — Question
Gujarat BoardEnglish MediumSTD 12 ScienceMathsStraight line in space2 Marks
Question
Write the vector equation of a line given by $\frac{\text{x}-5}{3}=\frac{\text{y}+4}{7}=\frac{\text{z}-6}{2}.$
✓
Answer
We have $\frac{\text{x}-5}{3}=\frac{\text{y}+4}{7}=\frac{\text{z}-6}{2}$ The given line passes through the point (5, -4, 6) and has direction ratios proportional to 3, 7, 2. Vector equation of the given line passing through the point having position vector $\vec{\text{a}}=5\hat{\text{i}}-4\hat{\text{j}}+6\hat{\text{k}}$ and parallel to a vector $\vec{\text{b}}=3\hat{\text{i}}+7\hat{\text{j}}+2\hat{\text{k}}$ is $\vec{\text{r}}=\vec{\text{a}}+\lambda\vec{\text{b}}$ $\Rightarrow\vec{\text{r}}=5\hat{\text{i}}-4\hat{\text{j}}+6\hat{\text{k}}+\lambda\big(3\hat{\text{i}}+7\hat{\text{j}}+2\hat{\text{k}}\big)$
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