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A vector has an x-component of 6.15m and a y-component of -3.88m. Find the magnitude and direction of the vector.

User Peter Baer
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1 Answer

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Final answer:

The magnitude of the vector is 7.27m and the direction is -31.3 degrees.

Step-by-step explanation:

The magnitude of a vector is found using the Pythagorean theorem. The magnitude, also known as the length, of a vector with x-component 6.15m and y-component -3.88m can be found as follows:

Magnitude = sqrt((x-component)^2 + (y-component)^2) = sqrt((6.15m)^2 + (-3.88m)^2) = sqrt(37.8225m^2 + 15.0544m^2) = sqrt(52.8769m^2) = 7.27m

The direction of a vector can be found using inverse tangent. The direction, also known as the angle, of a vector with x-component 6.15m and y-component -3.88m can be found as follows:

Direction = atan(y-component/x-component) = atan(-3.88m/6.15m) = atan(-0.631+b0) = -31.3 degrees (rounded to the nearest tenth)

User Nitesh Verma
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