1 11 2 Review of Vectors Recall A vector is a quantity that has both magnitude and direction A vector can be placed anywhere in the coordinate system without changing its value A vector placed at the origin corresponds to a unique point in the coordinate system Operations with Vectors All the basic operations and notation on 3 dimensional vectors are the same as 2 dimensional vectors as shown in the examples below Given a h6 0 2i and b 5i 3j 2k a b a b 2b a a b cos compa b proja b 1 Other Terms some new some old Direction Angles Direction Cosines Orthogonal Vectors Work Examples Given the points P 1 0 1 Q 2 3 1 and R 0 4 1 find P QR 2 Find a unit vector in the direction of the vector from 1 1 5 to 0 6 3 Consider the points P Q and R from the previous page Given the nonzero vector ha b ci is orthogonal to the vector from P to Q and the vector from R to Q find a b and c NOTE multiple answers possible 3
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