F a vector pq has its head at p x 1 y 1 and its tail

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(f) A vector -→ PQ has its head at P ( x 1 , y 1 ) and its tail at Q ( x 2 , y 2 ). Determine a formula for -→ PQ expressed in angular bracket notation.
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Math 254 Recitation Activity - Fall 2018 - Week 1 Page 2 of 4 (2) An ant walks due southeast at a speed of 2 centimeters per second on a flat sheet of paper. While the ant is walking, a person lifts the paper straight upward at 3 centimeters per second. Use a 3-dimensional vector to describe the velocity of the ant. (Positive x : east, positve y : north, positive z : up.) What is the speed of the ant? (3) A baseball initially travels in a direction 45 above the horizontal with a heading toward the northeast. If its speed is 80 mph, find the components of its initial velocity in east, north, and vertical directions. (Positive x : east, positve y : north, positive z : up.) (4) Let ~v = 2 ~ i + 3 ~ j - ~ k and ~w = ~ i - ~ j + 2 ~ k . Find the following: (a) ~v + 2 ~w . Give your answer in terms of the coordinate unit vectors ~ i , ~ j , ~ k and also using angular bracket notation. (b) | ~v | (c) Find a unit vector in the direction of ~v . (A unit vector is a vector with length 1.) (5) Two vectors are parallel if they are scalar multiples of each other. Find a vector that is parallel to ~v = h 3 , - 2 , 6 i having length 10. Find a second vector that has length 10 and is parallel to ~v = h 3 , - 2 , 6 i .
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Math 254 Recitation Activity - Fall 2018 - Week 1 Page 3 of 4 (6) The following problems are all using the same “hanging block” scenario described below.
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