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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
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.
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)
Why do nonperpendicular vectors need to be resolved into components before you can add the vectors together?
You can graphically add the vectors together without resolving them. However to mathematically add them they need to be resolved to find the new direction.
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 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
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 would you add two vectors that are not perpendicular or parallel?
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)
What are the applications of Parallelogram law of vectors?
The law is used to add vectors to find the resultant of two or more vectors acting at a point.
How you can add the vectors?
1) Graphically. Move one of the vectors (without rotating it) so that its tail coincides with the head of the other vector. 2) Analytically (mathematically), by adding components. For example, in two dimensions, separate each vector into an x-component and a y-component, and add the components of the different vectors.
