Question

Find the sum of the given vectors and illustrate geometrically. [0,1,2],[0,0,-3]

Answer 1

The sum of the given vectors is
`[0,1,2]+[0,0,-3]=[0,1,-1]`

Explanation:

For the given vectors (which are R³ vectors), the sum is simply the sum of each coordinate, if a general vector is written as

`[x,y,z]`

the sum of two vector will be in each coordinate at a time.

To illustrate geometrically the resulting vector in the space xyz

`[0,1,-1]`

we can say that the first coordinate is on the x-axis, the sencond on the y-axis, and the third one on the z-axis, so the illustration will be a vector starting from the center of coordinates, and ending in the coordinates 0 of the x-axis, 1 of the y-axis, and -1 of the z-axis. Or, in a plane yz (where x=0), a vector from the origin to the point 1 in y-axis, and -1 in z-axis.