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In Problems $27-32$, the vector $\mathbf{v}$ has initial point $P$ and terminal point $Q$. Write $\mathbf{v}$ in the form $a \mathbf{i}+b \mathbf{j}+c \mathbf{k}$; that is, find its position vector. $P=(3,2,-1) ; \quad Q=(5,6,0)$

   In Problems $27-32$, the vector $\mathbf{v}$ has initial point $P$ and terminal point $Q$. Write $\mathbf{v}$ in the form $a \mathbf{i}+b \mathbf{j}+c \mathbf{k}$; that is, find its position vector.
$P=(3,2,-1) ; \quad Q=(5,6,0)$
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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 29 ↓

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For this problem, $P = (3, 2, -1)$ and $Q = (5, 6, 0)$.  Show more…

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In Problems $27-32$, the vector $\mathbf{v}$ has initial point $P$ and terminal point $Q$. Write $\mathbf{v}$ in the form $a \mathbf{i}+b \mathbf{j}+c \mathbf{k}$; that is, find its position vector. $P=(3,2,-1) ; \quad Q=(5,6,0)$
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Key Concepts

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Standard Basis Vectors
The standard basis vectors (i, j, k) are unit vectors that point in the direction of the x-, y-, and z-axes respectively. They provide a convenient way to express any vector in three-dimensional space by scaling these fundamental directions.
Position Vector
A position vector represents the location of a point in space relative to an origin. It is commonly expressed in terms of its components along the coordinate axes (i, j, k) and is used to define vectors in a coordinate system.
Vector Subtraction
Vector subtraction is the process of finding the difference between two vectors. When determining the vector from one point to another, subtract the coordinates of the initial point from the coordinates of the terminal point, yielding the components of the displacement vector.

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