1. Section 10.7

2.  Multiply like components together, then add u 1 v 1 + u 2 v 2 Length of a vector: Angle between Vectors Theorem:

3.  Two nonzero vectors u and v are orthogonal iff their dot product is zero.

4.  A passenger jet is cruising at a speed of 300 knots in a direction 25˚ east of south and there is a 40 knot wind coming from the southwest. By how many degrees will the jet be thrown off course?  Jet’s velocity vector: [300, 295]  Wind velocity vector: [40, 45]  Component: 300cos295 + 40 cos 45 300 sin 295 + 40 sin 45

5. Component: 300cos295 + 40 cos 45 300 sin 295 + 40 sin 45 (155.0697, -243.608) Put back in polar form: R = 288.776 θ = -57.5˚ So the plane is getting “pushed” 7.48˚ off course.

6. Calculate the dot product of and -1 * -5 + 8* -10.2 5 – 81.6 -76.6

7.  Find the measure of the angle between the vectors u = and v = Formula:

8.  Explain the relationship between the dot product of two vectors and the angle between them.  If the dot product is positive, the angle is acute  If the dot product is negative, the angle is obtuse  If the dot product is zero, the angle is right.

9.  Describe all vectors in the plane that are orthogonal to and have length 4. Two equations: 0 = 17v 1 + 5v 2 16 = v 1 2 + v 2 2 Solve for v 2 in the first: v 2 = -17/5 v 1 Substitute back in: 16 = v 1 2 + (-17/5v 1 ) 2 16 = v 1 2 + (289/25)v 1 2 16 = 314/25v 1 2 400/314 = v 1 2

10. Two equations: 0 = 17v 1 + 5v 2 16 = v 1 2 + v 2 2 Solve for v 2 in the first: v 2 = -17/5 v 1 Plug back in:

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