Day 3: Adding Vectors
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Two or more vectors can be added together to find a single vector, called the resultant.
Vectors can be added by applying one vector after the other.
Two vectors can be added using the head-to-tail method or the parallelogram method.
We will be using the head-to-tail method.
Given two parallel vectors, 𝑢
⃗ and 𝑣 , in the same direction, |𝑢
⃗ +𝑣 | = |𝑢
⃗ | + |𝑣 | and 𝑢
⃗ + 𝑣 is in the
same direction as 𝑢
⃗ and 𝑣 .
Given two parallel vectors, 𝑢
⃗ and 𝑣 , with opposite directions and |𝑢
⃗ | > |𝑣 , |, |𝑢
⃗ + 𝑣 , | = |𝑢
⃗ | - |𝑣 , |
and 𝑢
⃗ + 𝑣 , is in the same direction as 𝑢
⃗.
⃗ , has zero magnitude and no specific direction. Adding two opposite vectors
The zero vector, 0
results in the zero vector.
For any vectors 𝑢
⃗ , 𝑣 , and 𝑤
⃗⃗ :
𝑢
⃗ +𝑣=𝑣+𝑢
⃗
(Commutative Property)
(𝑢
⃗ + 𝑣) + 𝑤
⃗⃗ = 𝑢
⃗ + (𝑣 + 𝑤
⃗⃗ )
(Associative Property)
⃗ =𝑣=0
⃗ +𝑣
𝑣+0
(Identity Property)
We can think of vectors as displacements.
Example 1:
Determine the distance and the displacement for the given 'trip' from A to B.
distance =
displacement =
Adding two vectors is finding a single displacement.
Example 2:
Draw the resultant vector.
Vector Addition using the Head - to - Tail Method:
Example 3:
Draw the resultant vector using the head - to - tail method.
Example 4:
Express one vector as the sum of the other two vectors.
Example 5:
Determine the magnitude and direction of the resultant vector 𝑎 + 𝑏⃗ .