Question

If two vectors \(\vec{r}.\vec{n_1}=d_1\) and \(\vec{r}.\vec{n_2}=d_2\) are such that \(\vec{n_1}.\vec{n_2}\)=0, then which of the following is true?

(a) The planes are perpendicular to each other

(b) The planes are parallel to each other

(c) Depends on the value of the vector

(d) The planes are at an angle greater than 90°

This question was posed to me in semester exam.

I want to ask this question from Three Dimensional Geometry topic in section Three Dimensional Geometry of Mathematics – Class 12

Answer 1

The correct answer is (a) The planes are perpendicular to each other

Easy explanation: We know that if the scalar or dot product of vectors is 0, then they are at right angles to each other. Here the dot product of the normal vectors of the plane is 0, i.e. \(\vec{n_1}.\vec{n_2}\)=0. Hence, the planes will be perpendicular to each other.