A vector \vec{n} of magnitude 8 units is inclined to the x-axis is | Filo

Class 12

Math

3D Geometry

Three Dimensional Geometry

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150

A vector of magnitude units is inclined to the x-axis is , y-axis at and an acute angle with the z-axis. If a plane passes through a point and is normal to , find its equation in vector form.

Solution:
If and are the angles made by the line segment with the coordinate axis.
and are called as the direction cosines and are usually denoted by and
and

Here , and let . Then,

We know that .
.
So, the equation of the plane is
.
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