Problem: Two vectors of equal magnitude A make an angle theta with each other. Find the magnitude of the resultant and direction of the resultant.

Solution:
Step 1: Draw the diagram showing the two vectors A making an angle theta with each other.

Step 2: Find the horizontal and vertical components of each vector. Since the vectors are of equal magnitude, their horizontal and vertical components will also be equal.



Step 3: Add the horizontal components and vertical components of each vector separately to find the total horizontal and vertical components.

Total horizontal component = 2A cos(theta)

Total vertical component = 2A sin(theta)

Step 4: Use the Pythagorean theorem to find the magnitude of the resultant.

Magnitude of resultant = sqrt[(total horizontal component)^2 + (total vertical component)^2]
= sqrt[(2A cos(theta))^2 + (2A sin(theta))^2]
= sqrt[4A^2(cos^2(theta) + sin^2(theta))]
= 2A

Step 5: Find the direction of the resultant by using the tangent function.

tan(theta) = total vertical component/total horizontal component
tan(theta) = 2A sin(theta)/2A cos(theta)
tan(theta) = tan(theta)
Therefore, the direction of the resultant is the same as the direction of the vectors, which is theta.

Final Answer: The magnitude of the resultant is 2A and the direction of the resultant is theta.