Provide the vector for each of the following.

(a) The vector from (2, -7, 0) -  (1, - 3, - 5 )

(b) The vector from (1,-3,-5) - (2, - 7, 0)

(c) The position vector for ( - 90, 4)

Solution

(a) Keep in mind that to build this vector we subtract coordinates of the starting point from the ending point.

{1-2,-3 - (-7), -5 -0}

= {-1,4,-5}

(b) Same thing here

{2-1,-7 - (-3),0 - (-5)}

= {1, - 4, 5}

Note that the only difference among the first two is the signs are all opposite.  This dissimilarity is significant as it is this difference that tells us that the two vectors point in opposite directions.

(c) Not much to this one other than the acknowledging that the position vector of a point is nothing much more than a vector with the point's coordinates like its components.