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PRE CALCULUS – HOMEWORK 2.14

1. Find the distance between (2,5) and (4,-10).

2. The distance formula is related to what other formula. What shape is used that relates the two formulas?

3. Find the midpoint of (6,9) and (-10,13).

4. Explain what is happening when you find the midpoint of two points.

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PRE CALCULUS – HOMEWORK 2.15

Plot each point in a three-dimensional coordinate system.

1. (1,-2,-4)
/ 2. (3,2,1)

3. (-5,-4,-2)
/ 4. (-2,-5, 3)

5. A family from Wichita, Kansas is using a GPS devise to plan a vacation to Castle Rock, Colorado. According to the device, the coordinates for the family’s home are (37.70, 97.20, 433 m), and the coordinates to Castle Rock are (39.40, 104.80, 1981 m). Determine the halfway point between their home and Castle Rock. / 6. During a training session, the location of two F-18 fighter jets are represented by the coordinates (675, -121, 19300) and (-289, 715, 16100), where the coordinates are given in feet.
a. Determine the distance between the two jets.
b. To what location would on the fighter pilots have to fly the F-18 to reduce the distance between the two jets by half?

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PRE CALCULUS – HOMEWORK 2.16
Locate and graph each vector in space.
1. a = -4j + 4k
/ 2. b = -3i -3j- 2k

Find the component form and magnitude of a vector with the given initial and terminal points. Then find a unit vector is the same direction as the vector.
3. A (-5,-5,-9) B (11,-3,-1) / 4. A (-4,0,-3) B (-4,-8,9)
Find each of the following for a = -5,-4,3, b = 6,-2,-7, and c = -2,2,4
5. 6a – 7b + 8c / 6. 7a – 5b

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PRE CALCULUS – HOMEWORK 2.17

1. Lena throws a javelin due south at a speed of 19 miles per hour and at an angle of 480 relative to the horizontal. If the wind is blowing with a velocity of 12 miles per hour at an angle of S150E, find the vector that represents the resultant velocity of the javelin.

2. A submarine heading due west dives at a speed of 25 knots and an angle of decline of 550. The current is moving with a velocity of 4 knots at an angle of S200W. Find a vector that represents the resultant velocity of the submarine relative to the initial point of the dive.