**Vectors in 3D space**

When we deal with vectors in space, we have one more dimension. In the coordinate system, the *z-*axis which is perpendicular to the* xy* plane is added. The function and principle of vectors remain exactly the same in three dimensional space as it is within a two dimensional plane.

In the coordinate system below, the *x-*axis is red, the* y*-axis is green, and the* z*-axis is blue. The *z-*axis base vector is denoted by the letter k.

The vector shown in the figure, which has a position vector at a point of (-10,3,2), is

A vector in space can be thought of as a space diagonal of a rectangular prism. The above could be thought of as a triangle with edge lengths of 10, 3 and 2. In this case, the length of the space diagonal is

So the length is

In general the length of a 3D vector is

Vector *a* is

**Example 1**

Point *A(1,3,2)* and point* B(3,2,6)* are in *XYZ* space. Find the vector *AB.*

Draft the situation. The draft does not have to be drawn in the coordinate system.

The position vectors of *A* and* B *are

In this case, vector *AB* is obtained by going against the position vector of point *A* and along the position vector of point *B*.

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