Vector Components. Coordinates  Vectors can be described in terms of coordinates. 6.0 km east and 3.4 km south6.0 km east and 3.4 km south 1 m forward,

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Presentation transcript:

Vector Components

Coordinates  Vectors can be described in terms of coordinates. 6.0 km east and 3.4 km south6.0 km east and 3.4 km south 1 m forward, 2 m left, 2 m up1 m forward, 2 m left, 2 m up  Coordinates are associated with axes in a graph. y x x = 6.0 m y = -3.4 m

Ordered Set  The value of the vector in each coordinate can be grouped as a set.  Each element of the set corresponds to one coordinate.  The elements, called components, are scalars, not vectors.

Component Addition  A vector equation is actually a set of equations. One equation for each componentOne equation for each component Components can be added and subtracted like the vectors themselvesComponents can be added and subtracted like the vectors themselves

Scalar Multiplication  A vector can be multiplied by a scalar. For instance, walk twice as far as in the hiking example.For instance, walk twice as far as in the hiking example.  Scalar multiplication multiplies each component by the same factor.  The result is a new vector, always parallel to the original vector.

Component Subtraction  Multiplying a vector by  1 will create an antiparallel vector of the same magnitude.  Vector subtraction is equivalent to scalar multiplication and addition.

Use of Angles  Find the components of vector of magnitude 2.0 km at 60° up from the x-axis.  Use trigonometry to convert vectors into components. x = r cos  y = r sin  y x x = (2.0 km) cos(60°) = 1.0 km y = (2.0 km) sin(60°) = 1.7 km 60°

Components to Angles  Find the magnitude and angle of a vector with components x = -5.0 m, y = 3.3 m. next y x x = -5.0 m y = 3.3 m  = 33 o above the negative x-axis L  L = 6.0 m