# 3D Vector resultant

1. Jan 20, 2012

### suneyna

Hello All,

Please guide me to calculate the resultant of the following two 3D vectors.
vec1 =(-0.3960i,4.6660j,15.2610k)
vec2 =(-4.1230i,-13.2200j,17.9170k)

Thanks
Suneyna

2. Jan 20, 2012

### HallsofIvy

Staff Emeritus
First a matter of notation- don't use parens and commas and "i", "j", and "k". Either (a, b, c) or ai+ bj+ ck.

The "resultant" or sum of the vectors ai+ bj+ ck and ui+ vj+ wk is just (a+ u)i+ (b+ v)j+ (c+ w)k.

3. Jan 20, 2012

### suneyna

Thanks for the response and guiding me about the correct notation.
I calculated the resultant in the same way as you mentioned.
Now I want to ask you that is it possible that two 3d vectors pointing downwards (but both didn't lie in the same plane) can have their resultant in upward direction.

4. Jan 21, 2012

### dalcde

What do you mean by two 3d vectors not lying the the same plane? As far as I know, any two vectors must lie on the same plane (if all vectors point from the origin).

5. Jan 21, 2012

### suneyna

I don't know how to paste a figure in the thread to make my point clear. but i am writing my vectors coordinates as follows:

vec1 =(-0.3960,4.6660,15.2610)

vec2 =(-4.1230,-13.2200,17.9170), both originated from origin (0,0,0) and the resultant is: res =(-4.5190,-8.5540,33.1780)

So, am i calculating the resultant in the right way?
I am pretty confused with their (above two vectors and resultant) directions.

6. Jan 22, 2012

### jeo23

It's looks like you are doing the math correctly. However, I'm confused as to why you are confused. I don't see any vector that points downward.

7. Jan 22, 2012

### suneyna

Dear I am working on a structure in MATLAB and drawn a vector 1, which originates from origin(0,0,0) and pointing towards one end of the structure and hence calculate vec1 from the coordinate information of the structure itself as vec1 =(-0.3960,4.6660,15.2610). Now, If u draw it in MATLAb or on some graphical tool, you will get the direction as i said.
Similarlily, I calculated vector 2 as vec2 =(-4.1230,-13.2200,17.9170), I know it is also, originated from origin so from the magnitude itself you can draw this vector too.

Now, I am thinking that the resultant vector res =(-4.5190,-8.5540,33.1780) should lie in between these two vectors, originating from origin and should points downwards as seen in above two (but not sure).

I am confused as this seems to be correct in 2d but for 3d i m not sure.
So I want your suggestion to be sure that i am working in right direction or not?