# Finding the Resultant Vector(Edexcel A Level Physics)

## Revision Note

Expertise

Physics

• Vectors can be combined by adding or subtracting them to produce the resultant vector
• The resultant vector is sometimes known as the ‘net’ vector (eg. the net force)

• There are two methods that can be used to add vectors
• Calculation – if the vectors are perpendicular
• Scale drawing – if the vectors are not perpendicular

#### Combining Vectors Using a Scale Diagram

• There are two methods that can be used to combine vectors using a scale diagram: the triangle method and the parallelogram method
• To combine vectors using the triangle method:
• Step 2: the resultant vector is formed by connecting the tail of the first vector to the head of the second vector

• To combine vectors using the parallelogram method:
• Step 1: link the vectors tail-to-tail
• Step 2: complete the resulting parallelogram
• Step 3: the resultant vector is the diagonal of the parallelogram

#### Worked example

Draw the vector c = a + b

#### Worked example

Draw the vector c = a – b

#### Combining Vectors by Calculating

• Combining vectors by calculation is a two-step process
• Finding the direction of the resultant using trigonometry
• Finding the magnitude of the resultant using Pythagoras

The magnitude of the resultant vector is found by using Pythagoras’ Theorem

• The direction of the resultant vector is found from the angle it makes with the horizontal or vertical
• The question should imply which angle it is referring to (ie. Calculate the angle from the x-axis)

• Calculating the angle of this resultant vector from the horizontal or vertical can be done using trigonometry
• Either the sine, cosine or tangent formula can be used depending on which vector magnitudes are calculated

The direction of vectors is found by using trigonometry

#### Worked example

A swimmer is crossing a river by swimming due north at 2 m s−1. The current flows east at 5 m s−1.

Determine the resultant velocity of the swimmer's motion.

Step 1: Sketch a diagram, including all known values

Step 2: Calculate the magnitude of the resultant using Pythagoras

= 5.4

Step 3: Calculate the angle using trigonometry

θ = 21.8

Step 4: Write the answer in full giving both magnitude and direction of the velocity and all units

The swimmer's velocity is 5.4 ms-1 at 22o to the horizontal direction

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