To find the unit vector divide by the norm (magnitude) which is,Originally Posted by Ranger SVO
Thus,
In the opposite direction means that is a negative of the vector.
Multiply by (-1) to get,
.
I was doing good until I got to the last two problems.
14. Give a unit vector that points in the opposite direction to the vector
-i + 2k
16. Find two nonparallel vectors that are perpendicular to i - j + k
I would like an explination alot more than an answer
Any vector perpendicular (orthogonal) to another has its dot porduct zero.Originally Posted by Ranger SVO
Thus, you want to find a vector perpendicular to the given one.
If the components of the first vector are
Then, you need that, (dot product)
The second vector has components of
Then you need that, (dot product)
And they are not parrallet meaning and are not (scalar) multiples of each other.
There a infinitely many solutions to the first and second equation.
One such solution is,
Note they are not multiples.
Thus,