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In Problems 29-36, the vector $\mathbf{v}$ has initial point $P$ and terminal point $Q$. Write $\mathbf{v}$ in the form $a \mathbf{i}+b \mathbf{j} ;$ that is, find its position vector. $P=(3,2) ; \quad Q=(5,6)$ 

   In Problems 29-36, the vector $\mathbf{v}$ has initial point $P$ and terminal point $Q$. Write $\mathbf{v}$ in the form $a \mathbf{i}+b \mathbf{j} ;$ that is, find its position vector.
 $P=(3,2) ; \quad Q=(5,6)$
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry
Michael Sullivan 4th Edition
Chapter 8, Problem 31 ↓

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For this problem, \( P = (3, 2) \) and \( Q = (5, 6) \).  Show more…

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In Problems 29-36, the vector $\mathbf{v}$ has initial point $P$ and terminal point $Q$. Write $\mathbf{v}$ in the form $a \mathbf{i}+b \mathbf{j} ;$ that is, find its position vector. $P=(3,2) ; \quad Q=(5,6)$
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Key Concepts

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Position Vector
A position vector describes the directed line segment from one point to another in a coordinate system. It is found by subtracting the coordinates of the initial point from those of the terminal point, resulting in a vector that indicates both the magnitude and direction of the displacement.
Vector Subtraction
Vector subtraction is the process of finding the difference between two vectors, typically used to determine the displacement from an initial point to a terminal point. In coordinate geometry, this involves subtracting the corresponding components of the vectors.
Cartesian Unit Vectors
Cartesian unit vectors, commonly denoted as i and j, represent the standard basis in a two-dimensional coordinate system. Any vector in the plane can be expressed as a linear combination of these unit vectors, where each coefficient is the magnitude of the vector's component in that direction.
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