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Objectives: Find the unit vector in the direction of v.

6.6 Day 2. Objectives: Find the unit vector in the direction of v. Write a vector in terms of its magnitude & direction Solve applied problems involving vectors. Pg. 691 # 40-52 (even), 66-74 (even). A Unit Vector has the same direction as a given vector, but is 1 unit long.

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Objectives: Find the unit vector in the direction of v.

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  1. 6.6 Day 2 • Objectives: • Find the unit vector in the direction of v. • Write a vector in terms of its magnitude & direction • Solve applied problems involving vectors Pg. 691 # 40-52 (even), 66-74 (even)

  2. A Unit Vector has the same direction as a given vector, but is 1 unit long • Unit vector = (original vector)/length of vector • Given vector, v = -2i + 7j, find the unit vector:

  3. 1. Find the unit vector in the same direction as v = 4i – 3j. Then, verify that the vector has magnitude (length) 1.

  4. Writing a Vector in terms of its Magnitude & Direction • v is a nonzero vector. The vector makes an angle measured from the positive x-axis to v, and we can talk about the magnitude & direction angle of this vector: This is a vector in a form almost exactly like polar form. The main distinction is that the vector is not affixed to the origin.

  5. Velocity Vector: vector representing speed & direction of object in motion • Example: The wind is blowing 30 miles per hour in the direction N20oE. • Express its velocity as a vector v. • If the wind is N20oE, it’s 70 degrees from the positive x-axis, so the angle=70 degrees and the magnitude is 30 mph.

  6. 2. The jet stream is blowing at 60 miles per hour in the direction S45oE. Express its velocity as a vector v in terms of i and j.

  7. 3. Two forces F1 and F2, of magnitude 30 and 60 pounds, respectively, act on an object. The direction of F1 is N10oE and the direction of F2 is N60oE. Find the magnitude, to the nearest hundredth of a pound, and the direction angle, to the nearest tenth of a degree, of the resultant force. Finding a Resultant Force Use the provided formulas:

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