The x component of a displacement vector

r is −149 m, while its y component is
−174 m.

(a) Find the magnitude of r.

(b) Find the direction of r.

To find the magnitude (or length) of vector r, we can use the Pythagorean theorem. The Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

(a) Finding the magnitude of r:
In this case, the x component of r is -149 m and the y component is -174 m. We can form a right triangle with these two components as the sides.

Using the Pythagorean theorem, we have:
Magnitude of r = sqrt((-149)^2 + (-174)^2)

Calculating this expression gives us the magnitude of r.

(b) Finding the direction of r:
To find the direction of vector r, we need to find the angle it makes with the positive x-axis. We can use trigonometry to solve for this angle.

To find the direction, we use the tangent of the angle:
tan θ = y/x

In this case, θ represents the angle between vector r and the positive x-axis, and x and y represent the respective components of vector r.

Calculating this expression gives us the direction of vector r in degrees or radians, depending on the unit preference.

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