# Given two vectors \overrightarrow A= 4.00i + 7.00j and \overrightarrow B= 5.00i - 2.00 j, find...

## Question:

Given two vectors {eq}\overrightarrow A= 4.00i + 7.00j \text{ and } \overrightarrow B= 5.00i - 2.00 j, {/eq} find the magnitude of each vector?

## Vector:

Vector: These quantities have magnitude as well as direction. These quantities are incomplete without direction.

The examples of vector quantities are force, displacement, etc. These quantities do require direction and are incomplete without direction.

Let's assume the vector is denoted by,

{eq}\vec{A} = A_{x} \hat{i}+A_{y} \hat{j} {/eq}

The magnitude of the vector is given by,

{eq}A=\sqrt{A_{x}^{2}+A_{y}^{2}} {/eq}

Given:

Vector, {eq}\overrightarrow A= 4.00i + 7.00j \text{ and } \overrightarrow B= 5.00i - 2.00 j, {/eq}

Calculation:

Comparing the given vectors with {eq}\vec{A} = A_{x} \hat{i}+A_{y} \hat{j} {/eq} we get,

{eq}A_{x}=4.00, A_{y}=7.00 {/eq} and {eq}B_{x}=5.00, B_{y}=-2.00 {/eq}

The magnitude of vector A is

{eq}A=\sqrt{A_{x}^{2}+A_{y}^{2}} = \sqrt{4.00^{2}+7.00^{2}} = 8.06 unit {/eq}

The magnitude of vector B is

{eq}B=\sqrt{B_{x}^{2}+B_{y}^{2}} = \sqrt{5.00^{2}+(-2.00)^{2}} = 5.385 unit {/eq}

The magnitude of A is 8.06 unit and magnitude of vector B is 5.385 unit.