Under which condition is the addition of two vectors maximum and minimum?
Question: Under which condition is the addition of two vectors maximum and minimum?
The addition of two vectors depends on their direction and magnitude:
Maximum Condition
The addition of two vectors is maximum when the vectors are in the same direction. In this case, their magnitudes add up directly. Mathematically, if vectors A and B are in the same direction:
∥ 𝐴 + 𝐵 ∥ = ∥ 𝐴 ∥ + ∥ 𝐵 ∥
Minimum Condition
The addition of two vectors is minimum when the vectors are in the exact opposite directions. Here, their magnitudes subtract from each other. Mathematically, if vectors A and B are in opposite directions:
∥ 𝐴+𝐵 ∥ = ∥ ∥ 𝐴 ∥ − ∥ 𝐵 ∥ ∥
These conditions explain the extremes of vector addition, illustrating how directionality plays a critical role in vector arithmetic.
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