Find the magnitude and direction angle of the vector v. V=6j
To find the magnitude and direction angle of a vector, we can use its components. The vector v has a y-component of 6 units, and no x-component (since it is purely in the y-direction).
1. Magnitude: The magnitude of a vector is calculated using the Pythagorean theorem. In this case, since there is no x-component, the magnitude of vector v is equal to the magnitude of its y-component, which is 6 units.
2. Direction Angle: To calculate the direction angle of a vector, we use the inverse tangent function (arctan or atan) with the ratio of the y-component to the x-component. Since the x-component is zero, the direction angle is either 90° (pi/2 radians) if the y-component is positive or -90° (-pi/2 radians) if the y-component is negative. In this case, since the y-component is 6 (positive), the direction angle is 90° (pi/2 radians).
Therefore, the magnitude of vector v is 6 units and the direction angle is 90° (pi/2 radians).