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Vector addition is commutative so you can start with either vector.
The graphical solutions are quite simple.
If the vectors are parallel, then their addition is the sum of the two vectors and acts in the same direction.
If the vectors are anti-parallel, then their addition is the difference of the two vectors and acts in the direction of the larger vector.
If the vectors are not parallel, draw them with their tails together. The complete the parallelogram using these as two of the sides. The addition of the vectors is the diagonal through the first vertex.
Otherwise, (and more accurately),
if you have vectors a and b inclined at angles p and q to the positive direction of the x axis, then the component of their sum along the
horizontal direction is s = a*cos(p) + b*cos(q)
and the vertical component is t = a*sin(p) + b*sin(q)
The magnitude of the resultant is sqrt(s2 + t2) and its direction is arctan(t/s) within the appropriate range.
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How do you add vectors using the component method?
1) Separate the vectors into components (if they are not already expressed as components). 2) Add each of the components separately. 3) If required, convert the vectors back to some other form. For twodimensional vectors, that would polar form.
When adding two vectors at right angles is the resultant of the vectors the algebraic sum of the two vectors?
No. Vectors add at rightangle bythe pythagoran theorem: resultant sum = square root of (vector 1 squared + vector 2 squared)
Can the resultant magnitude of 2 vectors be smaller than either of the vectors?
Yes. As an extreme example, if you add two vectors of the same magnitude, which point in the opposite direction, you get a vector of magnitude zero as a result.
Why can't we add or subtract vectors like scalars?
Because scalars do not take in the direction but just the magnitude while vectors can. You can add vectors ONLY if they are in the same direction.
How do you add two vectors that aren't parallel or perpendicular?
To add two vectors that aren't parallel or perpindicular you resolve both of the planes displacement vectors into "x' and "y" components and then add the components together. (parallelogram technique graphically)AnswerResolve both of the planes displacement vectors into x and y components and then add the components
Is it possible to add any 2 vectors?
Yes, it is possible to add any two vectors as long as they have the same number of dimensions. The result of adding two vectors is a new vector whose components are the sum of the corresponding components of the original vectors.
How do you add vectors using the component method?
1) Separate the vectors into components (if they are not already expressed as components). 2) Add each of the components separately. 3) If required, convert the vectors back to some other form. For twodimensional vectors, that would polar form.
Can you add equal vectors?
Yes, you can add vectors of equal length. Make sure they are equal by both of them having the same magnitude and direction. Otherwise, you can add equal vectors.
What is the sum of 2 vectors?
To find the sum of two vectors, you add their corresponding components together. For example, if you have two vectors A = (3, 5) and B = (2, -1), the sum would be A + B = (3 + 2, 5 + (-1)) = (5, 4).
When adding two vectors at right angles is the resultant of the vectors the algebraic sum of the two vectors?
No. Vectors add at rightangle bythe pythagoran theorem: resultant sum = square root of (vector 1 squared + vector 2 squared)
Can the resultant magnitude of 2 vectors be smaller than either of the vectors?
Yes. As an extreme example, if you add two vectors of the same magnitude, which point in the opposite direction, you get a vector of magnitude zero as a result.
Why can't we add or subtract vectors like scalars?
Because scalars do not take in the direction but just the magnitude while vectors can. You can add vectors ONLY if they are in the same direction.
What is the objectives of Resolution of Vectors?
One common reason why you need to do this is to add vectors. If you have two different vectors, and want to add them - algebraically, of course - then you first need to separate them into components. After you do that, you can easily add the components together.
How can you add vectors?
To add vectors, add their corresponding components together. If the vectors are in 2D, add the x-components together and the y-components together. If they are in 3D, add the x, y, and z-components accordingly. This will result in a new vector representing the sum of the original vectors.
What are the different methods in adding vectors?
Vectors can be added using the component method, where you add the corresponding components of the vectors to get the resultant vector. You can also add vectors using the graphical method, where you draw the vectors as arrows and then add them tip-to-tail to find the resultant vector. Additionally, vectors can be added using the trigonometric method, where you use trigonometry to find the magnitude and direction of the resultant vector.
Can three parallel vectors of uneven magnitude add to zero?
Yes - if you accept vectors pointing in opposite directions as "parallel". Example: 3 + 2 + (-5) = 0
How do you add two vectors that aren't parallel or perpendicular?
To add two vectors that aren't parallel or perpindicular you resolve both of the planes displacement vectors into "x' and "y" components and then add the components together. (parallelogram technique graphically)AnswerResolve both of the planes displacement vectors into x and y components and then add the components
