MHB Find the angle between 2 vectors w=i+3j, vector v=<5, 2>

Thread starter Elissa89
Start date Dec 10, 2018
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Angle Vector Vectors

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To find the angle between vectors w = i + 3j and v = <5, 2>, first calculate the cosine of the angle using the dot product formula. The cosine can be derived from the formula cos(θ) = (w · v) / (||w|| ||v||). Once the cosine is determined, the sine can be found using the Pythagorean identity sin(θ) = √(1 - cos²(θ)). This method allows for the complete determination of the angle between the two vectors. Understanding both sine and cosine is essential for solving problems involving vector angles.

Dec 10, 2018

Elissa89

I know how to find the cos(theta) between two vectors but I do not know how to find the sin(theta).

vector w=i+3j

vector v=<5, 2>

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Dec 11, 2018

skeeter

Elissa89 said:

I know how to find the cos(theta) between two vectors but I do not know how to find the sin(theta).

vector w=i+3j

vector v=<5, 2>

find the cosine, then use a form of the Pythagorean identity ...

$\sin{t} = \sqrt{1-\cos^2{t}}$

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