Question

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

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

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 49

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We need to find the unit vector in the same direction as the vector \(\mathbf{v} = i + j + k\). A unit vector is a vector of length 1. Show more…

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

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Key Concepts

Normalization

Normalization is the process of converting a non-zero vector to a unit vector by dividing each of its components by its magnitude. This operation preserves the original direction of the vector while setting its length to one.

Unit Vector

A unit vector is a vector that has a magnitude of one and is used to indicate direction. It simplifies many calculations in vector algebra as it conveys directional information independent of scale.

Vector Magnitude

The magnitude, or length, of a vector is calculated by taking the square root of the sum of the squares of its individual components. This measure is crucial for determining how to scale a vector during normalization.

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