Question

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. $P=(-3,2) ; \quad Q=(6,5)$ 

   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.
 $P=(-3,2) ; \quad Q=(6,5)$
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 32 ↓

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For this problem, $P$ is given as $(-3, 2)$ and $Q$ is given as $(6, 5)$. These coordinates represent the initial and terminal points of the vector $\mathbf{v}$, respectively.  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. $P=(-3,2) ; \quad Q=(6,5)$
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Key Concepts

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Component Form of a Vector
Expressing a vector in component form involves writing it as a sum of its horizontal (i) and vertical (j) parts. This form makes it easier to perform operations like addition, subtraction, and scalar multiplication on vectors in the coordinate plane.
Position Vector
A position vector represents the location of a point in space relative to an origin. In problems involving vectors between two points, it describes the displacement from one point to another and is key to understanding the direction and magnitude of the change between points.
Vector Subtraction
Vector subtraction is the process of finding the difference between two vectors by subtracting the corresponding components. When finding a displacement vector from an initial point to a terminal point, subtracting the coordinates of the initial point from the coordinates of the terminal point yields the vector's components.
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