Dot Product Problems Solution | Massachusetts Institute of Technology - Edubirdie

University:
Massachusetts Institute of Technology
Course:
18.02SC | Multivariable Calculus
Academic year:

2022
Views:

152

Pages:

1
Author:

Emerson Bowman

Dot product problems 1. a) Compute �1, 2, −4� · �2, 3, 5�. b) Is the angle between these two vectors acute, obtuse or right? Answer: a) �1, 2, −4� · �2, 3, 5� = 1 · 2 + 2 · 3 − 4 · 5 = −12. b) Let θ be the angle between the vectors. Since the dot product is negative we have cos θ < 0, which means θ > π/2. The angle is obtuse. 2. Suppose B = �2, 2, 1�. Suppose also that B makes an angle of 30◦ with A and A·B = 6. Find |A|. Answer: Since 300 = π/6 radians and |B| = 3 we get √ 3 4 6 = A · B = |A||B| cos(π/6) = |A| · 3 · ⇒ |A| = √ . 2 3 3. If A · B = 0 what is the angle between A and B? Answer: π/2.

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