Find by drawing and calculation the resultant of two vectors 3units and 4units inclined at each other
To find the resultant of two vectors using drawing and calculations, follow these steps:
Step 1: Draw the vectors
Start by drawing a horizontal line to represent the x-axis. From one end of the x-axis, draw the first vector, 3 units in length. Then, from the other end of the first vector, draw the second vector, inclined at an angle to the first vector, with a length of 4 units. Label the vectors accordingly.
Step 2: Draw a parallelogram
Using the head of the first vector as a reference point, draw a line parallel to the second vector. Similarly, using the head of the second vector as a reference point, draw a line parallel to the first vector. These lines should intersect, forming a parallelogram.
Step 3: Measure the diagonal
Next, measure the length of the diagonal line that connects the tails of both vectors within the parallelogram. This diagonal represents the resultant vector.
Step 4: Calculate the resultant vector
To calculate the magnitude of the resultant vector, you can use the Pythagorean theorem. The Pythagorean theorem states that the square of the hypotenuse (the diagonal in our case) is equal to the sum of the squares of the other two sides. In this case, the squares of the first vector (3 units) and the second vector (4 units) will be added to find the square of the resultant vector.
Thus, magnitude of the resultant vector = √[(3)^2 + (4)^2]
Calculating this expression gives us: magnitude of resultant vector = √(9 + 16) = √25 = 5 units.
Therefore, the magnitude of the resultant vector is 5 units.
Step 5: Determine the direction of the resultant vector
To find the direction of the resultant vector, you can use trigonometry. In this case, you can use the tangent of the angle between the resultant vector and the x-axis.
tanθ = (opposite/adjacent)
tanθ = (4/3)
Using inverse tangent (tan⁻¹) or arctan function, calculate the angle.
θ = tan⁻¹(4/3)
Calculating this expression gives us: θ ≈ 53.13°
Therefore, the resultant vector is 5 units in magnitude and inclined approximately 53.13° with the x-axis.