1 11.2: Review of VectorsRecall: A vector is a quantity that has bo th magnitude and direction. A vector can be placed any-where in the coordinate system without changing its value. A vector placed at the origin correspondsto a unique point in the coordinate system.Operations with Vectors: All the basic operations and no tation on 3-dimensional vectors are thesame 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 θ =compab =projab =1Other 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 QR2Find 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 orthogonalto the vector from P to Q and the vector from R to Q, find a, b, and c. (NOTE: multiple a
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