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HW.Vectors-v3

# HW.Vectors-v3 - Practice exercise Given the vectors a=(0...

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Practice exercise Given the vectors a= (0, 2, -1, 4, -1, 2) and b=( 3, 5, 6, 2, -2, -2) You can work out these things for yourself, and then check the answers in the box below Vector a+b Inner product <a|b> Length of a: |a| Length of b: |b| Cosine of the angle between them: cos ab The angle between them: ab ANSWERS TO PRACTICE: Vector a+b: (3, 7, 5, 6, -3, 0) Inner product <a|b>: 10 Length of a: |a| = 5.1 Length of b: |b| = 9.1 Cosine of the angle between them: .22 The angle between them: ab = 77 degrees. The following problems refer to these vectors: a = (1, 1, 3, 4) b= (4, -1, 3, 3 1. <a|b>= ? a. 12 b. 16 c. 20 d. 24 e. 28 2. |a|= ?

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3. |b|= ? 4. cos ab 5. The angle between the vectors a and b ab = a. 0 degrees b. 15 degrees c. 39 degrees d. 45 degrees e. 60 degrees 6. Are these two vectors perpendicular (that is, the angle between them is 90 degrees)? X=(2,3,4,0,0,0); Y=(0,0,0,2,3,4) a. Yes b. No 7. Are these two vectors perpendicular? X=(2,3,4,1,1,1); Y=(-1,-1,-1,2,3,4) a. Yes b. No
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