Two vectors having equal magnitude of 10 unit, have an angle of 60° between them. Find the magnitude of their resultant vector.
Question
Two vectors having equal magnitude of 10 unit, have an angle of 60° between them. Find the magnitude of their resultant vector.
Solution
Sure, here is the step by step solution:
Step 1: Identify the given values. The magnitude of both vectors is 10 units and the angle between them is 60°.
Step 2: Use the formula for the magnitude of the resultant vector when two vectors are given. The formula is:
R = √(a² + b² + 2abcosθ)
where a and b are the magnitudes of the vectors and θ is the angle between them.
Step 3: Substitute the given values into the formula:
R = √((10)² + (10)² + 21010*cos60°)
Step 4: Calculate the value inside the square root:
R = √(100 + 100 + 200*0.5)
Step 5: Simplify the expression:
R = √(200 + 100)
Step 6: Calculate the square root:
R = √300
Step 7: Simplify the square root:
R = 10√3 units
So, the magnitude of the resultant vector is 10√3 units.
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