Find the vector equation of a line passing through the point
Answer
Given: line passes through the point
To find: equation of line in vector and Cartesian forms
Formula Used: Equation of a line is
Vector form:
Cartesian form:
where
Explanation:
Here,
The direction ratios of the line are
\begin{array}{l}
\Rightarrow-4: 1:-1 \\
\Rightarrow 4:-1: 1
\end{array}
So,
Therefore,
Vector form:
\overrightarrow{\mathrm{r}}=3 \hat{\mathbf{i}}-2 \hat{\imath}+\hat{k}+\lambda(4 \hat{\imath}-\hat{\jmath}+\hat{k})
Cartesian form:
x–34=y+2–1=z–11\frac{x-3}{4}=\frac{y+2}{-1}=\frac{z-1}{1}