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### Course: Precalculus>Unit 6

Lesson 2: Vector components

# Introduction to vector components

Vectors are quantities that have a magnitude and a direction. In the two-dimensional plane, we can describe them in an equivalent way, by thinking about the changes in x and y from the vector's tail to its head. Created by Sal Khan.

## Want to join the conversation?

• Could I get a refresher on the 30-60-90 triangle rule?
• The ratio between them is 1:sqrt of 3:2 where 1 is the side opposite to 30 degree angle, sqrt of 3 is opposite to 60, and 2 to 90.
• What is the tail and head of a vector quantity?
• Tail of a vector is the initial (starting) point of a vector.

While, head of the vector is its opposite. Head of the vector simply means the vector's final (end point) point.
• Why do many of the practice/quiz problems state the vectors as "from the __ (ex. southward) direction" but actually are headed in that direction? Shouldn't the vector then be pointed north if it comes from the south?
• In physics, vectors are typically defined by their magnitude (length) and direction. The direction of a vector is usually given relative to a specific reference frame, such as north, east, south, and west.

When we say a vector is "from the southward direction," we mean that its direction is southward. So, the vector is pointing in the southward direction, not northward. In this case, the vector is pointing in the direction from which it originates, which is southward.

It's important to remember that the direction of a vector is independent of its position in space. So, even if a vector is positioned at a particular point, it still has a direction that is defined relative to a reference frame.
• Are two vectors with the same Δx and Δy, but different head and tail coordinate values the same vector?
• Yes, two vectors with the same Δx and Δy but different head and tail coordinate values would always be the same vector. This is true because vectors are defined solely by their magnitude and direction, and if they have the same Δx and Δy, they will also have the same magnitude and direction, and thus will be the same exact vector.