Multiplying Vectors in 3D Plane: Angles Explained

In summary: Calculationally, the angle is the dot product of the magnitude of the vector from one end to the other (in this case, the length of the vector from 3 to 4) and the vector from the other end to the first end (in this case, the length of the vector from 2 to 3).
  • #1
andrewkg
86
0
OK so I am a bit confused. I am doing multiplication of vectors. I am a bit confused about the angles between two vectors. Let's say a(vect)=(3.0)i-(4.0)j; b(vect)=(2.0)j+(3.0)k in unit vector notation. Or generally how are angles between two vectors in 3d defined. Not just in terms of the dot or cross equ.
 
Physics news on Phys.org
  • #2
It is not clear what your confusion is about.

Is it about the definition of the angle between two vectors?

Or is it about finding the angle between two vectors given their components?
 
  • #3
AFAIK, dot and cross products are how angles between vectors are determined, esp. in 3D. It's not like you are going to slap a protractor on them and read off the angle.
 
  • #4
Conceptually, the angle between two vectors is what you get if you put them together tail to tail and use a protractor to measure the angle that this forms. Calculationally, if you have the components of both vectors as in your example, equate the two common formulas for the dot product and solve for the angle:

$$A_x B_x + A_y B_y + A_z B_z = |\vec A||\vec B| \cos \theta$$
 
  • #5
Never mind I misread something earlier. Making my question very illogical. Sorry. Thanks though.
 
Last edited:
  • #6
andrewkg said:
I know how to find the angle between vectors. I know theta is ~110 just don't know where the ~110 deg comes from. By this I mean how is that angle defined. I just do not know how angle between vectors in a 3d plane are defined.

Conceptually, you put the two vectors together tail to tail as jtbell says above. The two vectors will lie in a single two-dimensional plane (which may be slanted/tilting); in that two-dimensional plane you can use a protractor to find the angle just as you would if you had started with vectors in only two dimensions.
 

FAQ: Multiplying Vectors in 3D Plane: Angles Explained

1. How do you multiply two vectors in three-dimensional space?

To multiply two vectors in three-dimensional space, you need to use the cross product or vector product. This involves taking the product of the magnitudes of the vectors and the sine of the angle between them. The result is a new vector that is perpendicular to both of the original vectors.

2. How do I find the angle between two vectors in 3D space?

To find the angle between two vectors in 3D space, you can use the dot product or scalar product. This involves taking the cosine of the angle between the vectors, and the result will be the angle in radians. Alternatively, you can use the cross product and take the inverse sine to find the angle in degrees.

3. Can you multiply a vector by a scalar in 3D space?

Yes, you can multiply a vector by a scalar in 3D space. This involves multiplying each component of the vector by the scalar, resulting in a new vector with a magnitude that is scaled by the scalar.

4. What is the significance of multiplying vectors in 3D space?

Multiplying vectors in 3D space has several applications in physics, engineering, and mathematics. It can be used to calculate torque, determine the direction of a magnetic field, and solve problems involving forces and motion in three dimensions.

5. Can you explain the difference between the cross product and dot product in 3D space?

The cross product and dot product are two different ways of multiplying vectors in 3D space. The cross product results in a new vector that is perpendicular to both of the original vectors, while the dot product results in a scalar value. The dot product measures the projection of one vector onto the other, while the cross product measures the area of the parallelogram formed by the two vectors.

Similar threads

I Why is the Cross Product Used in Mathematics? Understanding its Role and History
Replies
10
Views
1K
I What is the purpose of the vector α in the rotational work integral?
Replies
3
Views
948
I Calculating distance (from magnet) to an arbitrary point in 3D space
Replies
6
Views
1K
B A "no hands" rule for the cross product (requires literacy)
Replies
8
Views
1K
B Sign conventions in torque and non-uniform circular motion
Replies
1
Views
699
B Electric Flux - confused about integrating over a tilted area
Replies
8
Views
1K
I What are the significant angles between intersecting planes in 4D space?
Replies
26
Views
2K
Complete the parametric equation for the line where the planes cross
Replies
7
Views
1K
B Confusion about the angle between two vectors in a cross product
Replies
7
Views
2K
I The unit dyadic.A general expression for?
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top