Question

The equation of the plane passing through $(-1, 5, -7)$ and parallel to the plane $2x - 5y + 7z + 11 = 0$, is:

• A. $\vec{r} \cdot (2\hat{i} - 5\hat{j} - 7\hat{k}) + 76 = 0$
• B. $\vec{r} \cdot (2\hat{i} - 5\hat{j} + 7\hat{k}) + 76 = 0$
• C. $\vec{r} \cdot (2\hat{i} - 5\hat{j} + 7\hat{k}) + 75 = 0$
• D. $\vec{r} \cdot (2\hat{i} - 5\hat{j} + 7\hat{k}) + 65 = 0$
• E. $\vec{r} \cdot (2\hat{i} - 5\hat{j} - 7\hat{k}) + 55 = 0$

Hint:

To quickly find the constant, calculate the dot product of the normal vector $(2, -5, 7)$ and the point $(-1, 5, -7)$. The result is $-76$. Since the plane equation is $Ax+By+Cz = \text{constant}$, you get $2x - 5y + 7z = -76$, which simplifies to $+ 76 = 0$.

Answer 1

The Correct Option is B