NIMCET 2012 — Mathematics PYQ

1. Identify the given values:

• Point ($P$): $(x_1,y_1,z_1)=(1,2,3)$

• Normal Vector ($\vec{N}$): $A\hat{i}+B\hat{j}+C\hat{k}=3\hat{i}+1\hat{j}+2\hat{k}$

• Therefore, direction ratios of the normal are $A=3$, $B=1$, and $C=2$.

2. Use the Equation of the Plane formula:

The equation of a plane passing through $(x_1,y_1,z_1)$ with normal direction ratios $(A,B,C)$ is:

3. Substitute the values:

4. Simplify the equation:

Combine the constant terms:

Or,

Conclusion:

Based on the calculation, the equation is $3x+y+2z=11$.