Question

How do you write the ordered triple that represents $ TM $ given $ T\left( { - 2,4,7} \right) $ and $ M\left( { - 3,5,2} \right) $ ?

Answer 1

Hint: The two given points represent points in 3D geometry with x-,y- and z-coordinates as given in the corresponding brackets. $ TM $ will represent a vector drawn from point $ T $ to point $ M $ . To find the ordered triplet of $ TM $ we have to find the components of the vector that represents $ TM $ . This can be found as the difference of the corresponding elements of the given two points. For ordered triplet, order of the elements is important.

Complete step by step solution:
We have been given two points $ T $ and $ M $ in 3D geometry. The elements of the points are given as $ T\left( { - 2,4,7} \right) $ and $ M\left( { - 3,5,2} \right) $ respectively. The first element corresponds to x-coordinate, second element corresponds to y-coordinate and third element corresponds to z-coordinate.
We have found the ordered triplet that represents $ TM $ .
 $ TM $ is a vector drawn from the point $ T $ to point $ M $ .
The components of this vector will represent the triplet of the vector and when these components are written in order, we say it is an ordered triplet.
The components of the vector can be found as the difference of the corresponding elements of the given points.
Thus,
 $
  TM = M - T \\
   \Rightarrow TM = < - 3,5,2 > - < - 2,4,7 > \\
   \Rightarrow TM = < \left( { - 3} \right) - \left( { - 2} \right),\;5 - 4,\;2 - 7 > \\
   \Rightarrow TM = < - 1,1, - 5 > \;
  $
Hence, the ordered triplet that represents $ TM $ is $ < - 1,1, - 5 > $ .
So, the correct answer is “ $ < - 1,1, - 5 > $ ”.

Note: The order of the elements is important in an ordered triplet. We write first the x-component, then the y-component and then the z-component. When we are finding the difference of the components of the points we have to be careful that the starting point is reduced from the end point.