Final answer:
The magnitude of the resultant vector when two vectors with magnitudes of 60 and 80 units act at a 30° angle between them is 100 units by using vector addition and trigonometry. The correct answer from the options provided is A) Magnitude = 100 units, Direction = 30°.
Step-by-step explanation:
The magnitude and direction of the resultant vector, when two vectors with magnitudes of 60 units and 80 units act at a point with an angle of 30° between them, can be determined using vector addition. To find the magnitude of the resultant, we use the formula:
R = √(A² + B² + 2ABcosθ), where A and B are the magnitudes of the vectors, and θ is the angle between them. In this case:
A = 60 units
B = 80 units
θ = 30°
Plugging these values into the formula, we get:
R = √(60² + 80² + 2*60*80*cos30°)
By calculating this expression, we find that the magnitude of the resultant vector is 100 units. To find the direction, we would use trigonometry, but since this is not specified in the question, only the options given must be evaluated. Therefore, the answer is A) Magnitude = 100 units, Direction = 30°.