Question

In Problems 45-50, find the unit vector in the same direction as $\mathbf{v}$. $\mathbf{v}=2 \mathbf{i}-\mathbf{j}+\mathbf{k}$

   In Problems 45-50, find the unit vector in the same direction as $\mathbf{v}$.
 $\mathbf{v}=2 \mathbf{i}-\mathbf{j}+\mathbf{k}$

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 50

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The vector given is $\mathbf{v} = 2\mathbf{i} - \mathbf{j} + \mathbf{k}$. Show more…

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In Problems 45-50, find the unit vector in the same direction as $\mathbf{v}$. $\mathbf{v}=2 \mathbf{i}-\mathbf{j}+\mathbf{k}$

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Key Concepts

Unit Vector

A unit vector is a vector with a magnitude of 1 that retains the direction of the original vector. It is useful in specifying directions independently of the vector's magnitude.

Vector Magnitude

The magnitude of a vector is a measure of its length, calculated by taking the square root of the sum of the squares of its components. This value is essential when normalizing a vector.

Normalization

Normalization is the process of converting a vector to a unit vector by dividing each of its components by its magnitude. This procedure ensures that the direction of the vector is preserved while its length becomes 1.

Cartesian Components

Vectors expressed in Cartesian coordinates are broken into components along the i, j, and k axes. This format allows for clear representation and manipulation of the vector's directional and magnitude properties.

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