To add vectors graphically using arrows, you use the "head-to-tail" method: move the vectors so that the tail of the second vector starts at the head of the first vector. The resultant vector is then drawn from the tail of the first vector to the head of the second vector.
Here's a more detailed explanation:
1. Understanding Vectors and Arrows
- A vector has both magnitude (length) and direction.
- An arrow visually represents a vector. The length of the arrow corresponds to the vector's magnitude, and the arrow's orientation indicates the vector's direction.
2. The Head-to-Tail Method
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Step 1: Draw the First Vector: Represent the first vector (let's call it a) as an arrow.
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Step 2: Draw the Second Vector: Represent the second vector (let's call it b) as an arrow. Crucially, move vector b without changing its length or direction, so its tail starts at the head (arrow tip) of vector a.
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Step 3: Draw the Resultant Vector: The resultant vector (let's call it c) is the vector that starts at the tail of vector a and ends at the head of vector b. Draw an arrow representing vector c connecting these two points.
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Result: Vector c represents the sum of vectors a and b ( c = a + b).
3. Vector Subtraction
To subtract a vector b from a vector a (a - b), you first need to find the negative of vector b (-b). The negative of a vector has the same magnitude but the opposite direction.
- Step 1: Find -b: Reverse the direction of vector b.
- Step 2: Add a + (-b): Use the head-to-tail method as described above to add vector a and vector -b.
Example:
Imagine vector a represents a displacement of 5 meters to the East, and vector b represents a displacement of 3 meters to the North.
- Draw an arrow pointing East, representing vector a.
- Draw an arrow pointing North, representing vector b, with its tail starting at the tip of the first arrow.
- Draw an arrow from the starting point of the first arrow to the ending point of the second arrow. This new arrow is the resultant vector c, which represents the combined displacement. The magnitude and direction of c can then be measured (or calculated using trigonometry).
In summary, adding vectors with arrows involves visually placing them head-to-tail and drawing the resultant vector from the starting point to the ending point. This method allows for a geometric understanding of vector addition.
