Khan Academy Chapter 2 —— Vector

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Khan Academy

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Chapter 2 —— Vectors

Vector Basis

• A vector is a quantity that can be described as having both magnitude and direction

Equivalent Vectors

Components of vectors

Magnitude of Vectors

Scalar multiplication

Adding and subtracting vectors

Graphically Adding and subtracting vectors

Practice ：Graphically adding and subtracting vectors

Adding vectors algebraically & graphically

To add the vectors (x₁,y₁) and (x₂,y₂), we add the corresponding components from each vector: (x₁+x₂,y₁+y₂). Here’s a concrete example: the sum of (2,4) and (1,5) is (2+1,4+5), which is (3,9). There’s also a nice graphical way to add vectors, and the two ways will always result in the same vector…

Combined vector operations

Watch Sal find new vector 3u + 1/5w when u = (2, -1) and w = (-5, 5).

Vector operations review

Unit vectors intro

Unit vectors are vectors whose magnitude is exactly 1 unit. They are very useful for different reasons. Specifically, the unit vectors [0,1] and [1,0] can form together any other vector

Worked example: finding unit vector with given direction

Worked example: Scaling unit vectors

Watch Sal scale up a unit vector to have a magnitude greater than 1

Direction of vectors from components: 1st & 2nd quadrants

Sal first finds the direction angle of a vector in the first quadrant, then moves onto a trickier one in the second quadrant

Direction of vectors from components: 3rd & 4th quadrants

Sal finds the direction angle of a vector in the third quadrant and a vector in the fourth quadrant

Vectors forms review

Vector components from magnitude & direction

practice：

Vector components from magnitude & direction (advanced)

Vector magnitude and direction review