# Question Video: Finding the Direction Vector of a Straight Line Passing through Two Given Points Mathematics

Find the direction vector of the straight line passing through π΄ (1, β2, 7) and π΅ (4, β1, 3).

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### 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, weβre given the position vectors of two points in space, π΄ and π΅, and weβre asked to find the direction vector. When we want to find a direction vector ππ, 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, weβll have four subtract one, giving us three. Then weβll have negative one subtract negative two, which is equivalent to negative one plus two, which is one. And finally, weβll have three subtract seven, giving us negative four. And so weβve got the answer for the direction vector of π as three, one, negative four.

In this question, however, we didnβt necessarily need to find the direction vector ππ. We could also have found the direction vector ππ. In this case, we wouldβve got the vector inverse of π equals negative three, negative one, four, which would also have been a valid answer.