### Video Transcript

Find the direction vector of the
straight line passing through π΄ one, negative two, seven and π΅ four, negative one,
three.

In this question, weβre given the
position vectors of two points in space, π΄ and π΅, and weβre asked to find the
direction vector. When we want to find a direction
vector ππ, π΄ is the starting point and π΅ is the terminal point, we subtract the
starting point from the terminal point. In order to find the direction
vector, we can subtract each of the π₯-, π¦-, and π§-components in π΄ from those in
π΅. To begin then, weβll have four
subtract one, giving us three. Then weβll have negative one
subtract negative two, which is equivalent to negative one plus two, which is
one. And finally, weβll have three
subtract seven, giving us negative four. And so weβve got the answer for the
direction vector of π as three, one, negative four.

In this question, however, we
didnβt necessarily need to find the direction vector ππ. We could also have found the
direction vector ππ. In this case, we wouldβve got the
vector inverse of π equals negative three, negative one, four, which would also
have been a valid answer.