Select two axes in a 2-d plane along which you want the vector components (3 axes in 3-d and so on). The axes must meet at a point, but need not be perpendicular.
In 2-d, draw a parallelogram so that its diagonal is the given vector and the adjacent sides are parallel to the axes. These adjacent sides will represent the components of the vector.
If the axes are at right angles and the vector Vmakes an angle t with the positive horizontal axis, then
horizontal component = V*cost
and
vertical component = V*sint
prrpendicular projections of a vector called component of vector
The component of a vector x perpendicular to the vector y is x*y*sin(A) where A is the angle between the two vectors.
At what angle should a vector be directed to so that its x component is equal to its y component
Suppose the magnitude of the vector is V and its direction makes an angle A with the x-axis, then the x component is V*Cos(A) and the y component is V*Sin(A)
Two methods can be used for vector addition. (1) Graphically. Place the vectors head-to-tail, without changing their direction or size. (2) Analytically, that is, mathematically. Add the x-component and the y-component separately. The z-component too, if the vectors are in three dimensions.
The resultant vector describes the complete vector, magnitude and direction; while the component vector describes a single component of a vector, like the x-component. If the resultant vector has only one component, the resultant and the component are the same and there is no difference.t
resultant vector is a vector which will have the same effect as the sum of all the component vectors taken together.
Given the vector in angle-radius form? y-component=r sin(theta), x-component=r cos(theta)
no a vector cannot have a component greater than the magnitude of vector
If any component of a vector is not zero, then the vector is not zero.
No, a vector's component cannot be greater than the vector's magnitude. The magnitude represents the maximum possible magnitude of a component in any direction.
A vector component can never be greater than the vector's magnitude. The magnitude of a vector is the length of the vector and is always greater than or equal to any of its individual components.
No, a vector component is a projection of the vector onto a specific direction. It cannot have a magnitude greater than the magnitude of the vector itself.
prrpendicular projections of a vector called component of vector
-1, 2
No, a component of a vector cannot be greater than the magnitude of the vector itself. The magnitude of a vector is the maximum possible value that can be obtained from its components.
The component of a vector x perpendicular to the vector y is x*y*sin(A) where A is the angle between the two vectors.