Write the vector equation of the plane, passing through the point (a, b, c) and parallel to the plane vector(r) . (i + j + k) = 2.

Question

Write the vector equation of the plane, passing through the point (a, b, c) and parallel to the plane \(\vec{r}.(\hat{i}+\hat{j}+\hat{k}) = 2.\)

Answer 1

Since, the required plane is parallel to plane \(\vec{r}.(\hat{i}+\hat{j}+\hat{k}) = 2.\)

\(\therefore\) Normal of required plane is normal of given plane.

\(\Rightarrow\) Normal of required plane = \(\hat{i}+\hat{j}+\hat{k}\)

\(\therefore\) Required vector equation of plane