Final answer:
To find the magnitude and direction of the resultant and equilibrant of two forces, break down the forces into their x and y components. Add the x-components and y-components separately and find the resultant magnitude using the Pythagorean theorem. Use the inverse tangent function to find the resultant direction. For the equilibrant, use the same process with opposite directions.
Step-by-step explanation:
To find the magnitude and direction of the resultant of two forces, we can use vector addition. For the first force of 10 N acting in the N30°E direction, we can break it down into its x and y components using trigonometry. The x-component is 10 N * cos(30°) and the y-component is 10 N * sin(30°). For the second force of 15 N acting in the easterly direction, we can break it down into its x and y components as well.
To find the magnitude and direction of the resultant, we can add the x-components and the y-components separately. The magnitude of the resultant is found using the Pythagorean theorem: Resultant magnitude = sqrt((sum of x-component)^2 + (sum of y-component)^2). The direction of the resultant can be found using the inverse tangent function: Resultant direction = tan^(-1)((sum of y-component) / (sum of x-component)).
To find the magnitude and direction of the equilibrant, we can use the same process but with the opposite direction for each force.