Find the equation of the plane passing through the intersection of the planes $\vec{r} \cdot (2\hat{i} + 2\hat{j} - 3\hat{k}) = 7$ and $\vec{r} \cdot (2\hat{i} + 5\hat{j} + 3\hat{k}) = 9$ and through the point $(2, 1, 3)$.

Year	Paper Code	Set	Position
CBSE 2022	Series 65-6	Set 1	Question 11
CBSE 2022	Series 65-6	Set 2	Question 12
CBSE 2022	Series 65-6	Set 3	Question 13

• Step 1: Stating the fundamental formula / law statement (+1 Mark)
• Step 2: Intermediate mathematical substitution or proof steps (+1 Mark)
• Step 3: Correct final value or conclusion with mandatory SI units (+1 Mark)