# The x component of vector \vec{A} is -11.6 m and the y component is +55.1 m. (a) What is the...

## Question:

The x component of vector {eq}\vec{A} {/eq} is -11.6 m and the y component is +55.1 m.

(a) What is the magnitude of {eq}\vec{A} {/eq}?

(b) What is the angle between the direction of {eq}\vec{A} {/eq} and the positive direction of x?

## Magnitude and Direction of a Vector:

For a two-dimensional vector, the magnitude of can be calculated a,

{eq}|A| = \sqrt{A_x^2 + A_y^2} {/eq}

while the angle between the components that corresponds to the direction of the vector is given by,

{eq}\theta = \arctan(\Big{|}\frac{A_y}{A_x}\Big{|}) {/eq}

## Answer and Explanation:

_Part A:_

The magnitude of the {eq}\vec{A}{/eq} can be calculated as,

{eq}|A| = \sqrt{A_x^2 + A_y^2} = \sqrt{(-11.6 m)^ + (55.1 m )^2} = 56.31...

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#### Learn more about this topic:

from Common Entrance Test (CET): Study Guide & Syllabus

Chapter 57 / Lesson 3