Calculate Vector with Magnitude & Direction Given

[jimbo_durham]

Hi, i have a known magnitude to give my vector in an xy plane, and i have a desired direction. I need the (vx, vy, vz=0) to describe my vector. I am sure this can be done easily.

an example is,

i have a point at (10,10,0) in cartesian (x,y,z) and will use this as the starting point of my vector. This vector must have a magnitude of 4, and must be in a direction along the line connecting the point (10,10,0) with the origin (0,0,0).

ie my vector has the magnitude 5 and direciton that of a vector (-10,-10,0).

in this example the solution is simply to write

$$z^{2}=x^{2}+y^{2}$$, and as x=y,

$$\sqrt{ \frac{z^{2}}{2} }=x=3.5$$ ish.

giving me vector with components (3.5,3.5,0)

this however is in the wrong direction (need (-3.5,-3.5,0))

however if x=/=y, how is this solved? and how is the direction accounted for (+ve or -ve)?

 

[jimbo_durham]

for example a point at (10,9,0) with magnitude 5 along the vector from the point to the origin as before, which is now (-10,-9,0).

how do i find its components (vx, vy, vz=0)?

 

[sennyk]

Find the unit vector first

First, find the unit vector in your desired direction; then multiply by your desired magnitude.

The vector (-10, -10, 0) lies on your direction; Now find the unit vector in that direction. i.e. divide by the magnitude. Then multiply by 4.

 

[jimbo_durham]

excelent, works like a dream. thanks sennyk