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 4.1 What’s a Vector? 4.2 Vector Addition 4.3 Vector Subtraction 4.4 Multiplication by a Scalar 4.5 Vector Components

 4.6 Vector Multiplication 4.7 Key Formulas 4.8 Practice Questions 4.9 Explanations
There are bound to be several questions on SAT II Physics that involve vector addition, particularly in mechanics. The test doesn’t demand a very sophisticated understanding of vector addition, but it’s important that you grasp the principle. That is, you won’t be asked to make complicated calculations, but you will be expected to know what happens when you add two vectors together.
The easiest way to learn how vector addition works is to look at it graphically. There are two equivalent ways to add vectors graphically: the tip-to-tail method and the parallelogram method. Both will get you to the same result, but one or the other is more convenient depending on the circumstances.
Tip-to-Tail Method
We can add any two vectors, A and B, by placing the tail of B so that it meets the tip of A. The sum, A + B, is the vector from the tail of A to the tip of B.
Note that you’ll get the same vector if you place the tip of B against the tail of A. In other words, A + B and B + A are equivalent.
Parallelogram Method
To add A and B using the parallelogram method, place the tail of B so that it meets the tail of A. Take these two vectors to be the first two adjacent sides of a parallelogram, and draw in the remaining two sides. The vector sum, A + B, extends from the tails of A and B across the diagonal to the opposite corner of the parallelogram. If the vectors are perpendicular and unequal in magnitude, the parallelogram will be a rectangle. If the vectors are perpendicular and equal in magnitude, the parallelogram will be a square.
Of course, knowing what the sum of two vectors looks like is often not enough. Sometimes you’ll need to know the magnitude of the resultant vector. This, of course, depends not only on the magnitude of the two vectors you’re adding, but also on the angle between the two vectors.