Vectors in Three Dimensions 11.2 Vectors in Three Dimensions

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Example Let u = 2, −4, 1 and v = 3, 0, −1 . Find the components of the following vectors and draw them in ℝ3. a. 1 2 𝐮 b. −2𝐮 c. 𝐮+2v

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Example Consider the points P(5, 3, 1) and Q(−7, 8, 1). Express 𝑃𝑄 in terms of the unit vectors i, j, and k Find the magnitude of 𝑃𝑄 . Find the position vector of magnitude 10 in the direction of 𝑃𝑄 .

Example A plane is flying horizontally due north in calm air at 300 miles per hour when it encounters a horizontal crosswind blowing southeast at 40 miles per hour and a downdraft blowing vertically downward at 30 miles per hour. What is the resulting speed of the plane relative to the ground? (Finding direction will be presented in the next section.)

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