Video Transcript
Give a direction vector of the line
through the origin and the point six, six, one.
In this question, we are asked to
find the direction vector of a line passing through two points. The line passes through the origin,
which has coordinates zero, zero, zero and also through the point with coordinates
six, six, one, which we will call point 𝐴. We need to find the direction
vector of the line 𝐎𝐀.
We recall that to find the
direction vector 𝐀𝐁, where 𝐴 is the starting point and 𝐵 is the terminal point,
we subtract the position vector of the starting point from the position vector of
the terminal point. In this question, to find the
direction vector 𝐎𝐀, we subtract the vector zero, zero, zero from the vector six,
six, one. When subtracting vectors, we simply
subtract their corresponding components. This means that the direction
vector of the line is six, six, one.
It is worth noting that vector 𝐎𝐀
is always just the vector with components equal to the coordinates of 𝐴. It is also worth noting that we
were asked to give a direction vector that passes through the two points. This means that instead of
calculating 𝐎𝐀, we could have calculated the direction vector 𝐀𝐎. This would have given us the vector
negative six, negative six, negative one, which is the vector inverse of 𝐎𝐀.
