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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)
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.
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.
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
