Solving Vectors

MA1310: Week 7 Solving Vectors

This lab requires you to:

· Use magnitude and direction to show vectors are equal.

· Visualize scalar multiplication, vector addition, and vector subtraction as geometric vectors.

· Represent vectors in the rectangular coordinate system.

· Perform operations with vectors in terms of i and j.

· Find the unit vector in the direction of v.

· Write a vector in terms of its magnitude and direction.

· Solve applied problems involving vectors.

· Find the dot product of two vectors.

· Find the angle between two vectors.

· Use the dot product to determine if two vectors are orthogonal.

Answer the following questions to complete this lab:

1. What is a directed line segment?

2. What are equal vectors?

3. Let v be a vector from initial point P1 = (–11, –12) to terminal point P2 = (2, 5). Write v in terms of i and j.

4. Let u = 8i – 6j and v = –5i + 8j. Find the vector u + v.

5. Find the unit vector that has the same direction as the vector v = –12j.

6. A Boeing 737 aircraft maintains a constant speed of 500 miles per hour headed due south. The jet stream is 80 miles per hour in the northeasterly direction.

a. Express the velocity va of the 737 relative to the air, and the velocity vw of the jet stream in terms of i and j.

b. Find the velocity vg of the 737 relative to the ground. (Hint: vg = va + vw)

c. ( E W N S v w = velocity of jet stream v g v a = – 500j )Find the actual speed of the 737 relative to the ground. (Hint: )

7.