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PoutineIntergalactique9812

Bonsoir,

Est-ce que vous pouvez m’aider avec cette question? Merci beaucoup!!

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Louis-Philippe B

Thank you for your question!

The simplest way to answer this question is to solve the equation that establishes that the addition of vectors A and B equals (16,0). The simplest way to do this is to decompose both vectors into their components, and thus, develop two equations:

$$ \overline{A}cos(\theta) + \overline{B}cos(\theta) = 16 $$

$$ \overline{A}sin(\theta) + \overline{B}sin(\theta) = 0 $$

Simplifying both equations yields the following:

$$ cos(\theta)(\overline{A}+\overline{B}) = 16 $$

$$ sin(\theta)(\overline{A}+\overline{B}) = 0 $$

One can then input the dimensions of both vectors and solve for theta:

$$ cos(\theta)(10+10) = 16 $$

$$ cos(\theta) = 16/20 = 0.8 $$

$$ \theta = arccos(0.8) $$

$$ \theta ≈ 36.9° $$

There you go!

This Alloprof webpage explains vector components:

https://www.alloprof.qc.ca/en/students/vl/mathematics/vector-components-0-m1299

Don't hesitate to ask for more help!