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

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:

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

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.

Velocity Vector: vector representing speed & direction of object in motion Example: The wind is blowing 30 miles per hour in the direction N20 o E. Express its velocity as a vector v. If the wind is N20 o E, it’s 70 degrees from the positive x-axis, so the angle=70 degrees and the magnitude is 30 mph.

2. The jet stream is blowing at 60 miles per hour in the direction S45 o E. Express its velocity as a vector v in terms of i and j.

Finding a Resultant Force Use the provided formulas: 3. Two forces F 1 and F 2, of magnitude 30 and 60 pounds, respectively, act on an object. The direction of F 1 is N10 o E and the direction of F 2 is N60 o E. 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.