Find the equations of the planes passing through the line of intersection of the planes $\vec{r} \cdot (\hat{i} + 3\hat{j}) = 6$ and $\vec{r} \cdot (3\hat{i} - \hat{j} - 4\hat{k}) = 0$, which are at a distance of 1 unit from the origin.

Year	Paper Code	Set	Position
CBSE 2022	Series 65-4	Set 1	Question 11
CBSE 2022	Series 65-4	Set 2	Question 13
CBSE 2022	Series 65-4	Set 3	Question 12

• 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)