Quick question- if I know the magnitude of a certain vector, the coordinates of its tail (as an ordered triple), and that the vector itself is going in the same direction as another vector (given x/y/z coordinates of the other one), how can I find the components of the vector itself?
I got an answer but I don't think it's right because I can swap my values between x/y/z for it to work... but isn't there just 1 answer (only 1 possible x, y, and z component)?
I'll just make something up, so when I do the actual problems I still have to think lol
- They give the coordinates of the tail
- They give the magnitude
- They say the vector is in the same direction as u = (4, -3, -6)
I guess by direction they mean which way it is is moving (on positive or negative axis)...
From my made up question here, x is a positive direction while y and z are negative, so I guess that means that the vector that I'm finding has to have a positive x value but negative y and z values.
So a vector with the same direction as (4,,-3,-6) passing through (a,b,c) can be written as
We can find the magnitude
From here plug in the magnitude for M and solve the quadratic for the value of t and sub back into the original equation.
A vector with magnitude 5 and its tail at (0,0) in the direction (3,4)
well one possible answer would be the vector 3i +4j, but what is wrong with
-3i-4j these both have the same magnitude, but face the opposite way.
I guess it depends on how they define direction, you may just want to pick the positive one.
I did it another way. Does this work?
I took the vector given (the one that mine follows in the same direction). Then I converted it to a unit vector with magnitude 1. I multiplied the unit vector by a scalar of the magnitude given to come up with a new vector.
Then I separated that new vector into components.
Are the components I'm looking for:
a) The x, y, and z values when the vector has the tail at the origin?
b) The x, y, and z values of the tip?
I think the tail information is irrelevant.