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The diagram shows two vectors that point west and north. Two vectors added using the tip to tail method. There is a 12 meter vector west added to a 5 meter vector north in a right triangle. The hypotenuse is a dashed arrow labeled R. What is the magnitude of the resultant vector? 13 miles 17 miles 60 miles 169 miles

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skyluke89

The magnitude of the resultant vector is 13 meters

Explanation:

In this problem, we have the following vectors:

[tex]v_1 = 12 m[/tex] in the west direction

[tex]v_2 = 5 m[/tex] in the north direction

We notice that the two vectors are perpendicular to each other: so, they correspond to the sides of a right triangle, of which the resultant vector is the hypothenuse.

Therefore, it is possible to find the magnitude of the resultant vector simply by applying Pythagorean's theorem:

[tex]v=\sqrt{v_1^2+v_2^2}[/tex]

And  substituting the magnitudes of the two vectors, we find

[tex]v=\sqrt{12^2+5^2}=13 m[/tex]

So, the magnitude of the resultant is 13 meters.

Learn more about vector addition:

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oddawsomeman2004

Answer:

13

Explanation:

Using the formula A squared plus B squared equals C squared. By squaring 5, we get 25, and by squaring 12, we get 144. Adding these, we get 169. The square root of this is 13.

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