Given u = ⟨1, 3⟩, v = ⟨2, 1⟩, and cos(ϴ) = StartFraction StartRoot 2 EndRoot Over 2 EndFraction , where ϴ is the angle between the vectors, what is the scalar projection uv and the dot product u · v?

uv = 1.41 and u · v = 4.47
uv = 2.24 and u · v = 5.00
uv = 2.24 and u · v = 7.07
uv = 7.07 and u · v = 15.81

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glowfireflies2468 glowfireflies2468 · Answer 1 · 2021-01-06T06:07:26+01:00

Answer:

B. uv = 2.24 and u*v = 5.00

Step-by-step explanation:

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jainveenamrata jainveenamrata · Answer 2 · 2022-07-14T13:27:56+02:00

The scalar projection uv and the dot product u · v will be 2.24 and 5. Then the correct option is B.

The quantity which has magnitude, direction and follows the law of vector addition is called a vector.

Given u = ⟨1, 3⟩, v = ⟨2, 1⟩, and cos(θ) = √2 / 2, where θ is the angle between the vectors.

Then the scalar projection uv and the dot product u · v will be

The dot product will be

u·v = ⟨1, 3⟩·⟨2, 1⟩

u·v = 2 + 3

u·v = 5

Then the projection will be

uv = (u·v) / ||v||

uv = 5 / |√(2² + 1²)|

uv = 2.236 ≈ 2.24

Then the correct option is B.

More about the vector link is given below.

https://brainly.com/question/13188123

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