# Why can't the horizontal or vertical component equal the magnitude of the vector?

## Question:

Why can't the horizontal or vertical component equal the magnitude of the vector?

## Magnitude of A Vector:

For any vector (let's choose two dimensions without loss of generality), say {eq}\vec{A} = A_1 \hat{e}_1 + A_2 \hat{e}_2, {/eq}

the magnitude of this vector is given by:

{eq}|\vec{A}| = A = \sqrt{A^2_1 + A^2_2} {/eq}

## Answer and Explanation:

For any vector, {eq}\vec{A}, {/eq} with two non-zero components, the magnitude is given by:

{eq}|\vec{A}| = A = \sqrt{A^2_1 + A^2_2} {/eq}

The...

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How to Do Vector Operations Using Components

from UExcel Physics: Study Guide & Test Prep

Chapter 2 / Lesson 7
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