Given: The plane equation is:
\[ 3x + 2y + z = 6 \]
Step 1: Find the direction ratios
The line perpendicular to the plane has its direction ratios given by the coefficients of the plane equation:
\[ (3, 2, 1) \]
Step 2: Use the symmetric form equation
The equation of the required line passing through (7, 5, 3) and having direction ratios (3, 2, 1) is:
\[ \frac{x - 7}{3} = \frac{y - 5}{2} = \frac{z - 3}{1} \]
Final Answer:
\[ \frac{x-7}{3} = \frac{y-5}{2} = \frac{z-3}{1} \]
List - I | List - II | ||
(P) | γ equals | (1) | \(-\hat{i}-\hat{j}+\hat{k}\) |
(Q) | A possible choice for \(\hat{n}\) is | (2) | \(\sqrt{\frac{3}{2}}\) |
(R) | \(\overrightarrow{OR_1}\) equals | (3) | 1 |
(S) | A possible value of \(\overrightarrow{OR_1}.\hat{n}\) is | (4) | \(\frac{1}{\sqrt6}\hat{i}-\frac{2}{\sqrt6}\hat{j}+\frac{1}{\sqrt6}\hat{k}\) |
(5) | \(\sqrt{\frac{2}{3}}\) |