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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. $P=(0,0,0) ; \quad Q=(3,4,-1)$ 

   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.
$P=(0,0,0) ; \quad Q=(3,4,-1)$
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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 27 ↓

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In this problem, \( P = (0, 0, 0) \) and \( Q = (3, 4, -1) \).  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. $P=(0,0,0) ; \quad Q=(3,4,-1)$
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Key Concepts

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Vector Subtraction
In vector geometry, the vector connecting two points is found by subtracting the coordinates of the initial point from the coordinates of the terminal point. This operation, done component-wise, yields the components of the vector, demonstrating how displacement is computed in space.
Component Form of a Vector
The component form expresses a vector as a sum of its scalar components multiplied by the corresponding unit vectors. This form, written as a linear combination such as a i + b j + c k, clearly indicates the contribution of each directional axis to the overall vector, which is vital in applications such as physics and engineering.
Unit Vectors
Unit vectors are the building blocks of vector representation in a coordinate system, typically denoted as i, j, and k in three-dimensional space. They have a magnitude of one and point in the directions of the x, y, and z axes, respectively, allowing any vector to be decomposed into its directional components.
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the vector v initial position P and the terminal point Q. Write v in the form ai + bj; find its position vector. P= (-2,6) Q= (3,2)
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