Question

Math geniuses

pls help with this question!






and pls look at my other questions!!! tysm
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Answer 1

Problem 1, part (a)

`||v|| = √((-9)^2+(7)^2) = √(130)\\\\||w|| = √((7)^2+(5)^2) = √(74)\\\\\cos(\theta) = (v \cdot w)/(||v||*||w||)\\\\\cos(\theta) = ((-9)*(7)+7*5)/(√(130)*√(74))\\\\\cos(\theta) \approx (-28)/(98.081599)\\\\\cos(\theta) \approx -0.285477\\\\\theta \approx \cos^(-1)(-0.285477)\\\\\theta \approx 106.587363\\\\\theta \approx 107\\\\`

Answer: 107 degrees

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Problem 1, part (b)

The previous result (107) is neither 0, nor 90, nor 180. This means the vectors are neither parallel nor perpendicular.

Answer: Neither

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Problem 2, part (a)

We follow the same idea as problem 1, part (a). Just with different numbers of course.

`||u|| = √((-3)^2+(2)^2) = √(13)\\\\||r|| = √((-6)^2+(4)^2) = √(52)\\\\\cos(\theta) = (u \cdot r)/(||u||*||r||)\\\\\cos(\theta) = ((-3)*(-6)+2*4)/(√(13)*√(52))\\\\\cos(\theta) = (26)/(26)\\\\\cos(\theta) = 1\\\\\theta = \cos^(-1)(1)\\\\\theta = 0`

Answer: 0

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Problem 2, part (b)

The lines are parallel because of the angle of 0 degrees between the vectors. The angles point in the same direction.

Answer: Parallel