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 𝐴 (1, βˆ’2, 7) and 𝐡 (4, βˆ’1, 3).

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Video Transcript

Find the direction vector of the straight line passing through 𝐴 one, negative two, seven and 𝐡 four, negative one, three.

In this question, we’re given the position vectors of two points in space, 𝐴 and 𝐡, and we’re asked to find the direction vector. When we want to find a direction vector 𝐀𝐁, 𝐴 is the starting point and 𝐡 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‘₯-, 𝑦-, and 𝑧-components in 𝐴 from those in 𝐡. To begin then, we’ll have four subtract one, giving us three. Then we’ll have negative one subtract negative two, which is equivalent to negative one plus two, which is one. And finally, we’ll have three subtract seven, giving us negative four. And so we’ve got the answer for the direction vector of 𝐝 as three, one, negative four.

In this question, however, we didn’t necessarily need to find the direction vector 𝐀𝐁. We could also have found the direction vector 𝐁𝐀. In this case, we would’ve got the vector inverse of 𝐝 equals negative three, negative one, four, which would also have been a valid answer.

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