Question

A vector is a quantity that has magnitude and direction. For example, if you travel 20 miles northwest, 20 miles is the magnitude and northwest is the direction. In this example, the vector is called a displacement vector. Vectors often represent displacement, speed, acceleration, or force.You can think about a vector as a directed line segment. The initial point is the tail of the vector. The terminal point is the tip, usually represented by an arrowhead. The vector in the diagram can be named either

Answer 1

Part 1.

For a vector

`\vec{v}=\langle x,y\rangle`

its magnitude is written as

`|\vec{v}|`

and is given by

`|\vec{v}|=\sqrt[]{x^2+y^2}`

This formula comes from Pythagorean theorem:

Therefore, the answer for part A is:

`|\vec{v}|=\sqrt[]{x^2+y^2}`

Part B.

Now, we can use the above result into the given vector. Then, the magnitude of vector u is

`\begin{gathered} |\vec{u}|=\sqrt[]{4^2+7^2} \\ |\vec{u}|=\sqrt[]{16^{}+49} \\ |\vec{u}|=\sqrt[]{65} \\ |\vec{u}|=8.0623 \end{gathered}`

Then, the answer for part B is:

`|\vec{u}|=8.0623`