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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. $P=(1,1) ; \quad Q=(2,2)$ 

   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.
$P=(1,1) ; \quad Q=(2,2)$
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 36 ↓

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For this problem, \( P = (1, 1) \) and \( Q = (2, 2) \).  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. $P=(1,1) ; \quad Q=(2,2)$
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Key Concepts

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Position Vector
A position vector represents a point's location in a coordinate system by describing the displacement from the origin to that point using its components along the coordinate axes.
Vector Subtraction
Vector subtraction involves finding the difference between two vectors by subtracting their corresponding components, which is used to determine the vector that points from one specified point to another.
Unit Vectors
Unit vectors are standard basis vectors, commonly denoted as i and j in two-dimensional space, that indicate direction along the x-axis and y-axis, respectively; they are used to express any vector in terms of its horizontal and vertical components.
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