vector refresher part 2

Vector Refresher Part 2• Vector Addition• Multiplication by

Scalar Quantities• Graphical

Representations• Analytical Methods

Vector Addition• A lot of times, it’s important to know the

resultant of a set of vectors• The resultant vector can be described as the

sum of all the vector quantities you wish to evaluate

• We’ll look at graphical and analytical techniques for doing this

Graphical Methods For Vector Addition

• 2 ways to look at vector addition graphically• Parallelogram method

Connect the tails of both vectors to start.

Graphical Methods For Vector Addition

• 2 ways to look at vector addition graphically• Parallelogram method

Create a parallelogram with each vector as one of the sides.

Graphical Methods For Vector Addition

• 2 ways to look at vector addition graphically• Parallelogram method

The resultant goes from the place where 2 tails meet to the place where 2 heads meet

Graphical Methods For Vector Addition

• 2 ways to look at vector addition graphically• Head-to-tail method

With this method, the vectors are added by placing the tail of a vector at the head of another one to make a continuous path.

Graphical Methods For Vector Addition

• 2 ways to look at vector addition graphically• Head-to-tail method

The addition of these vectors results in a vector that starts at the tail of the first vector and ends at the head of the final vector

Graphical Methods For Vector Addition

• 2 ways to look at vector addition graphically• Head-to-tail method

If we had a 3rd vector, we could add it to the previous result

Graphical Methods For Vector Addition

• 2 ways to look at vector addition graphically• Head-to-tail method

If we had a 3rd vector, we could add it to the previous result

Multiplying a Vector By a Scalar

When a vector is multiplied by a scalar, the length of the vector can be elongated or shortened. If the scalar is a negative number, the direction is reversed.

Multiplying a Vector By a Scalar

When a vector is multiplied by a scalar, the length of the vector can be elongated or shortened. If the scalar is a negative number, the direction is reversed.

Multiplying a vector by 2 yields a vector with the SAME DIRECTION and twice the length

Multiplying a Vector By a Scalar

When a vector is multiplied by a scalar, the length of the vector can be elongated or shortened. If the scalar is a negative number, the direction is reversed.

Multiplying a vector by 1/2 yields a vector with the SAME DIRECTION and half the length

Multiplying a Vector By a Scalar

When a vector is multiplied by a scalar, the length of the vector can be elongated or shortened. If the scalar is a negative number, the direction is reversed.

Multiplying a vector by -1 yields a vector with the OPPOSITE DIRECTION and the same length

ExampleDraw

Start by multiplying vector A by 1/2

ExampleDraw

Start by multiplying vector A by 1/2

ExampleDraw

Next, multiply vector B by -3

ExampleDraw

Now add these vectors together

ExampleDraw

The resultant vector is shown in green

Analytical Method for Vector Addition

When vectors are added to each other, the components in each direction are summed.

Analytical Method for Vector Addition

When vectors are added to each other, the components in each direction are summed.

Analytical Method for Vector Addition

When vectors are added to each other, the components in each direction are summed.

Multiplying a Vector By a Scalar

When multiplying a vector by a scalar, the scalar must be applied to each component of the vectorThus, if we multiply by a scalar “k”, we get:

The first thing to do is determine F3

ExampleDetermine the resultant force caused by the following 3 force vectors.

The first thing to do is determine F3

ExampleDetermine the resultant force caused by the following 3 force vectors.

The first thing to do is determine F3

ExampleDetermine the resultant force caused by the following 3 force vectors.

The first thing to do is determine F3

ExampleDetermine the resultant force caused by the following 3 force vectors.

The first thing to do is determine F3

ExampleDetermine the resultant force caused by the following 3 force vectors.

The first thing to do is determine F3

ExampleDetermine the resultant force caused by the following 3 force vectors.

The first thing to do is determine F3

ExampleDetermine the resultant force caused by the following 3 force vectors.

Now we can add the 3 vectors together to determine the resultant force

ExampleDetermine the resultant force caused by the following 3 force vectors.

Now we can add the 3 vectors together to determine the resultant force

ExampleDetermine the resultant force caused by the following 3 force vectors.

Now we can add the 3 vectors together to determine the resultant force

ExampleDetermine the resultant force caused by the following 3 force vectors.

Don’t forget the units, they’re as important to the answer as the numbers are

ExampleDetermine the resultant force caused by the following 3 force vectors.

Don’t forget the units, they’re as important to the answer as the numbers are

ExampleDetermine the resultant force caused by the following 3 force vectors.