The vector that is normal to the plane defined by the points (3, 0, 0), (0, 1, 0), and (0, 0, 4) is

Question

Quizplus · Accepted Answer

To find a vector normal to the plane defined by three points, you can take two vectors that lie in the plane, find their cross product, and normalize it if necessary. Using points (3, 0, 0), (0, 1, 0), and (0, 0, 4), we can form two vectors: vector AB = (-3, 1, 0) and vector AC = (-3, 0, 4). The cross product of AB and AC gives us a vector normal to the plane, which is (4, -12, 3). Normalizing this vector gives us $\frac { 4 } { 13 } i - \frac { 12 } { 13 } j + \frac { 3 } { 13 } k$, making choice A correct.

The Vector That Is Normal to the Plane Defined by the Points