Calculating 3D Vector Resultant - Suneyna

In summary, the conversation is about calculating the resultant of two 3D vectors and the correct notation for writing vectors. The formula for calculating the resultant of two vectors is also mentioned. The person asks if it is possible for two 3D vectors pointing downwards to have a resultant in the upwards direction. The expert clarifies that all vectors must lie on the same plane and there is no vector pointing downwards in the given example. The person then explains their confusion and asks for the expert's suggestion on whether they are working in the right direction or not.
  • #1
suneyna
5
0
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
 
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  • #2
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
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
suneyna said:
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.

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
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
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
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?
 

FAQ: Calculating 3D Vector Resultant - Suneyna

How do you calculate the magnitude of a 3D vector resultant?

To calculate the magnitude of a 3D vector resultant, you need to use the Pythagorean theorem, which states that the square of the magnitude is equal to the sum of the squares of the individual components. In other words, you need to square the x, y, and z components of the vector, add them together, and then take the square root of the result.

What is the difference between a scalar and a vector quantity?

A scalar quantity is a physical quantity that has only magnitude, such as mass or temperature. On the other hand, a vector quantity has both magnitude and direction, such as velocity or force. In the context of 3D vector resultant, the magnitude represents the scalar quantity, while the direction represents the vector quantity.

How do you calculate the direction of a 3D vector resultant?

To calculate the direction of a 3D vector resultant, you need to use trigonometry. First, find the angles between the resultant vector and each of the three axes (x, y, and z). Then, use a trigonometric function, such as tangent or cosine, to determine the direction of the resultant vector.

Can a 3D vector resultant have a negative magnitude?

Yes, a 3D vector resultant can have a negative magnitude. This occurs when the individual components of the vector have opposite signs, such as a positive x-component and a negative y-component. In this case, the resultant vector will have a negative magnitude and will be directed towards the negative quadrant of the coordinate system.

What is the significance of calculating a 3D vector resultant?

Calculating a 3D vector resultant is important in many scientific and engineering applications. It allows us to combine multiple vectors into a single vector and determine its overall magnitude and direction. This is particularly useful in fields such as physics, mechanics, and computer graphics, where vector operations are commonly used to model and analyze physical systems.

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