Is it possible to add any 2 vectors?

Updated: 9/23/2023
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Q: Is it possible to add any 2 vectors?
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What should be the angle between 2 vectors a?

The angle between 2 vectors can have any value.

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.

Is it possible to add three vectors of equal magnitudes and get zero?

Of course it is! for example, [1, √3] + [-2, 0] + [1, - √3 ] = [0, 0]. Like this example, all other sets of such vectors will form an equilateral triangle on the graph.. Actually connecting the endpoints of the 3 vectors forms the equilateral triangle. The vectors are actually 120° apart.

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.

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 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.

Can the sum of magnitudes of two vectors ever be equal to the magnitude of the sum of these two vectors?

Sure, if the two vectors point in the same direction.When we need the sum of magnitudes of two vectors we simply add the magnitudes, but to get the magnitude of the sum of these two vectors we need to add the vectors geometrically.Formula to find magnitude of the sum of these two vectors is sqrt[ |A|2 +|B|2 +2*|A|*|B|*cos(z) ] where |A| and |B| are magnitudes of two A and B vectors, and z is the angle between the two vectors.Clearly, magnitude of sum of two vectors is less than sum of magnitudes(|A| + |B|) for all cases except when cos(z)=1(for which it becomes = |A| + |B| ). Cos(z)=1 when z=0, i.e. the vectors are in the same direction(angle between them is 0).Also if we consider addition of two null vectors then their sum is zero in both ways of addition.So, we get two caseswhen the two vectors are in same direction, andwhen the two vectors are null vectors.In all other cases sum of magnitudes is greater than magnitude of the sum of two vectors.

How are vectors subtracted?

In order to subtract (or add vectors), you must define your frame of reference. Vectors have magnitude and direction. so they are define on an x, y, and z axis. Once the vector is referenece by it's x-y-z components (either positive or negative), then you add/subtract them just like any other number. example v1= 3x + 5y + 5z and v2=2x+3y + 2z so, V1-V2= (3-2)x + (5-3)y + (5-2)z, which reduces to x+2y+3z

The resultant between 2 vectors can be found by placing the vectors?


What is the difference between coplanar vectors and collinear vectors?

The term collinear is used to describe vectors which are scalar multiples of one another (they are parallel; can have different magnitudes in the same or opposite direction). The term coplanar is used to describe vectors in at least 3-space. Coplanar vectors are three or more vectors that lie in the same plane (any 2-D flat surface).

Explain what is meant by a concurrent vectors?

A vector has 2 components - it's magnitude and direction. Concurrent vectors are 2 vectors that have the same direction but may have different magnitudes.