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Vector Components

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

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Vector Components

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  1. Vector Components

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

  3. 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.

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

  5. Scalar Multiplication • A vector can be multiplied by a scalar. • 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.

  6. 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.

  7. 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 Use of Angles y = (2.0 km) sin(60°) = 1.7 km 60° x = (2.0 km) cos(60°) = 1.0 km

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

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