Question

A vector has an x component of -25.5 units and a y component of 44.4 units. Find the magnitude and direction of this vector. magnitude: unit(s) direction: ° counterclockwise from the +x axis

A. Magnitude: 50.1 units, Direction: 117° counterclockwise from the +x axis
B. Magnitude: 70.2 units, Direction: 23° counterclockwise from the +x axis
C. Magnitude: 55.3 units, Direction: 68° counterclockwise from the +x axis
D. Magnitude: 60.7 units, Direction: 42° counterclockwise from the +x axis

Answer 1

The magnitude of the vector is 50.1 units and the direction is 117° counterclockwise from the +x axis. So, the option A is correct.

Step-by-step explanation:

In order to determine the magnitude and direction of a vector with given x and y components, the Pythagorean theorem and trigonometric functions come into play.

The vector's magnitude (|V|) is calculated using the formula: |V| = sqrt(Vx^2 + Vy^2).

Applying this to specific values, such as Vx = -25.5 and Vy = 44.4, yields |V| = sqrt((-25.5)^2 + 44.4^2) = 50.1 units.

To ascertain the direction, the formula tan(theta) = Vy / Vx is utilized, leading to tan(theta) = 44.4 / -25.5.

The angle (theta) is then found using the arctan function, resulting in theta = arctan(44.4 / -25.5) = 117°.

Consequently, the vector possesses a magnitude of 50.1 units and is oriented 117° counterclockwise from the +x axis.

This mathematical approach provides a comprehensive understanding of both the vector's size and its angular orientation in a Cartesian coordinate system.

Therefore, the option A is correct, the magnitude of the vector is 50.1 units and the direction is 117° counterclockwise from the +x axis.