Warm Up 1)Find the magnitude and direction of a vector with initial point (-5, 7) and terminal point (-1, -3). 2)Find, in simplest form, the unit vector.

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Presentation transcript:

Warm Up 1)Find the magnitude and direction of a vector with initial point (-5, 7) and terminal point (-1, -3). 2)Find, in simplest form, the unit vector in the direction of 4i – 2j. 3)Given v of magnitude 200 and direction 215°, and w of magnitude 150 and direction 162°, find v + w.

Homework Questions?????

More Vectors

A plane is flying on the bearing N 65  E at 500mph. Express the velocity of the plane as a vector. The wind is blowing in the direction N 25  W at 80mph. Express the velocity of the wind as a vector. Determine the actual speed and direction of the plane.

A plane must actually fly due south at a constant speed of 675mph against a headwind of 60mph blowing in the direction N 15  E. What direction and speed must the pilot maintain to stay on course?

The Dot Product Unlike addition and scalar multiplication with vectors, the dot product of vectors is a scalar.

Determine the dot product of the vectors

Let v =,u = and w = Find the indicated quantity

The angle between two vectors, u and v.

Find u v, where φ is the angle between u and v. 1)|u| = 8, |v| = 10, φ = 150°. 2)|u| = 2, |v| = 3, φ = 60° 3)| u | = 4, |v| = 1, φ = 90°.

Find the angle between the vectors 1) and 2) and 3) and

If the angle between two vectors is 90°, the vectors are orthogonal.

Are the vectors orthogonal, parallel, or neither? 1) and 2) and 3) and

Think about it.. What is true about the angle between two nonzero vectors u and v, if the following are true? u v = 0 u v < 0 u v > 0 v = ku, where k is a scalar

Non-calculator Use the dot product or scalar multiplication to describe the angle between the vectors as acute, obtuse, right, 0° or 180° and explain. and 1) 2) 3)