PYQ NEET- Three Dimensional Geometry
- Question: Find the equation of the plane passing through the point (1, 2, 3) and perpendicular to the line $\vec{r} = \hat{i} + \hat{j} - 2\hat{k} + \lambda (2\hat{i} - \hat{j} + 3\hat{k})$.
Answer: The vector $\vec{n} = (2\hat{i} - \hat{j} + 3\hat{k})$ is perpendicular to the plane. The equation of the plane can be written as $\vec{r} \cdot \vec{n} = d$, where $d$ is a constant. Substituting the point (1, 2, 3) into the equation, we get $d = 15$. Therefore, the equation of the plane is $\vec{r} \cdot (2\hat{i} - \hat{j} + 3\hat{k}) = 15$.
- Question: Find the distance between the parallel planes $2x - y + 2z = 8$ and $4x -
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