A line passes through (2, –1, 3) and is perpendicular to the lines vector(r) = (i + j - k) + λ (2i - 2j + k)

Question

A line passes through (2, –1, 3) and is perpendicular to the lines

\(\vec{r}=\hat{i}+\hat{j}-\hat{k}+\lambda (2\hat{i}-2\hat{j}+\hat{k})\) and \(\vec{r}=(2\hat{i}-\hat{j}-3\hat{k})+\mu (\hat{i}+2\hat{j}+2\hat{k}).\) Obtain its equation in vector and cartesian form.

Answer 1

Let \(\vec{b}\) be parallel vector of required line.

\(\Rightarrow\) \(\vec{b}\) is perpendicular to both given line.

Hence, the equation of line in vector form is

Equation in cartesian form is