Describe the characteristics of a vector diagram

Create vector diagrams for perpendicular vectors

Calculate the magnitude and direction of a resultant vector

Vectors can be represented graphically using scaled vector diagrams. In these diagrams, vectors are

represented by arrows that point in the direction of the vector.

The length of the vector arrow is proportional to the vector’s magnitude

1. A scale is clearly listed2. A vector arrow (with arrowhead) is drawn

in a specified direction. The vector arrow has a head and a tail.

3. The magnitude and direction of the vector is clearly labeled.

The direction of a vector can be expressed as a counterclockwise angle of rotation of the vector about its “tail" from due East. A vector with a direction of 240 ° means that if

the tail of the vector was pinned down, the vector would be rotated 240 ° counterclockwise from due east.

The direction of a vector can also be expressed as an angle of rotation from a specific direction

For example, a vector can be said to have a direction of 40 degrees North of East This means the vector pointing East has

been rotated 40 degrees towards the northerly direction

The magnitude of a vector in a scaled vector diagram is depicted by the length of the arrow.

The displacement from the tail of the first vector to the head of the last vector is called the resultant

For vectors that are perpendicular to one another, the Pythagorean theorem and the inverse tangent function can be used to determine the magnitude and direction of the resultant vector

The Pythagorean theorem can be used to find the magnitude of the resultant (hypotenuse) if you know the magnitude of both the x and y components

Hypotenuse2 = Length leg one2 + Length of leg two2

Resultant

The inverse tangent function can be used to find the direction of the resultant› For any right triangle, the tangent of an angle is

defined as the ratio of the opposite and adjacent legs

Angle = tan-1 (opposite leg (y) / adjacent leg (x))

A squirrel trying to get down a tree travels 2.5 m east across a branch and then 17 m down the tree. What is the magnitude and direction of the squirrel’s displacement? 24 m 81.6˚ S or E