Vector systems are a branch of mathematics that is used to manipulate measurements that have a value as well as a direction. Common examples are velocity, acceleration, force, etc - measurements involving motion. However, some motion-related measurements are not vectors. Distance, speed are not.
The smallest magnitude resulting from the addition of vectors with individual magnitudes of 4 and 3 is 1, obtained when the directions of the two component vectors are 180 degrees apart.
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.
The vectors can not be both equal, but they can have the same magnitude of 3, if they are at a 60 degree angle.
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.
Vectors and Scolars Vectors: have an magnitude and a direction Scolars: have an magnitude but have no direction
No, vectors and scalars are not the same. Vectors have both magnitude and direction, while scalars only have magnitude. Examples of vectors include velocity and force, while examples of scalars include speed and temperature.
Vector systems are a branch of mathematics that is used to manipulate measurements that have a value as well as a direction. Common examples are velocity, acceleration, force, etc - measurements involving motion. However, some motion-related measurements are not vectors. Distance, speed are not.
The smallest magnitude resulting from the addition of vectors with individual magnitudes of 4 and 3 is 1, obtained when the directions of the two component vectors are 180 degrees apart.
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.
the measurements are 3 in.
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).
The vectors can not be both equal, but they can have the same magnitude of 3, if they are at a 60 degree angle.
Coplanar vectors lie within the same plane, meaning they can be represented by arrows with their tails at the same point. Collinear vectors, on the other hand, lie along the same line, meaning they have the same or opposite directions. In essence, coplanar vectors can be parallel or intersecting within the same plane, while collinear vectors are always parallel or antiparallel along the same line.
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.
You do the dot product of the vectors by multiplying their corresponding coordinates and adding them up altogether. For instance: <1,2,3> ∙ <-3,4,-1> = 1(-3) + 2(4) + 3(-1) = -3 + 8 - 3 = 2
No it is not. It's possible to have to have a set of vectors that are linearly dependent but still Span R^3. Same holds true for reverse. Linear Independence does not guarantee Span R^3. IF both conditions are met then that set of vectors is called the Basis for R^3. So, for a set of vectors, S, to be a Basis it must be:(1) Linearly Independent(2) Span S = R^3.This means that both conditions are independent.