Drawing Vectors
In order to draw a vector accurately we must represent its magnitude properly and include a reference direction in the diagram. A scale allows us to translate the length of the arrow into the vector's magnitude. For instance if one chooses a scale of 1 cm = 2 N ...
Drawing Vectors
In order to draw a vector accurately we must represent its magnitude properly and include a reference direction in the diagram. A scale allows us to translate the length of the arrow into the vector's magnitude. For instance if one chooses a scale of \(\text{1}\) \(\text{cm}\) = \(\text{2}\) \(\text{N}\) (\(\text{1}\) \(\text{cm}\) represents \(\text{2}\) \(\text{N}\)), a force of \(\text{20}\) \(\text{N}\) towards the East would be represented as an arrow \(\text{10}\) \(\text{cm}\) long pointing towards the right. The points of a compass are often used to show direction or alternatively an arrow pointing in the reference direction.
Method: Drawing Vectors
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Decide upon a scale and write it down.
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Decide on a reference direction
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Determine the length of the arrow representing the vector, by using the scale.
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Draw the vector as an arrow. Make sure that you fill in the arrow head.
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Fill in the magnitude of the vector.
Example 1
Question
Draw the following vector quantity: \(\vec{v} = \text{6}\text{ m·s$^{-1}$}\) North
Step 1: Decide on a scale and write it down.
\(\text{1}\) \(\text{ cm}\) = \(\text{2}\) \(\text{m·s$^{-1}$}\)
Step 2: Decide on a reference direction
Step 3: Determine the length of the arrow at the specific scale.
If \(\text{1}\) \(\text{cm}\) = \(\text{2}\) \(\text{m·s$^{-1}$}\), then \(\text{6}\) \(\text{m·s$^{-1}$}\) = \(\text{3}\) \(\text{cm}\)
Step 4: Draw the vector as an arrow.
Scale used: \(\text{1}\) \(\text{cm}\) = \(\text{2}\) \(\text{m·s$^{-1}$}\)
Example 2
Question
Draw the following vector quantity: \(\vec{s} = \text{16}\text{ m}\) east
Step 1: Decide on a scale and write it down.
\(\text{1}\) \(\text{cm}\) = \(\text{4}\) \(\text{m}\)
Step 2: Decide on a reference direction
Step 3: Determine the length of the arrow at the specific scale.
If \(\text{1}\) \(\text{cm}\) = \(\text{4}\) \(\text{m}\), then \(\text{16}\) \(\text{m}\) = \(\text{4}\) \(\text{cm}\)
Step 4: Draw the vector as an arrow
Scale used: \(\text{1}\) \(\text{cm}\) = \(\text{4}\) \(\text{m}\)
Direction = East
This lesson is part of:
Vectors and Scalars