# The concept of a vector valued function r t x t i y t

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the concept of a vector-valued function, r ( t ) = x ( t ) i + y ( t ) j derivatives of vector-valued functions, velocity and speed, and acceleration integrating vector-valued functions

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2 solving initial value problems for vector-valued functions Key topics from § 9.4: the formula for the trajectory of an object moving in the plane with a launch angle of α radians, an initial speed of v 0 , and initial position ( x 0 , y 0 ). the maximum height, flight time, and range of the object moving in the plane as just described Key topics from § 10.1: vectors in R 3 and the standard unit vectors, i , j , and k addition and scalar multiplication for vectors in R 3 length and unit vectors in R 3 the distance between two points in space the midpoint of the line segment between two points in space the equation of a sphere with a given center and radius Key topics from § 10.2: the definition of, and the formula for, the dot product of two vectors in R 3 the Law of Cosines the formula for the projection of one vector on another the definition of the cross product of two vectors in R 3 ( | u × v | and the direction of u × v the determinant formula for the cross product of two vectors in R 3 the area of a the triangle formed by three points in R 3
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