Let Ā and B be the two vectors of magnitude 10 units each .if they inc...
Explanation:
Finding the Components of the Vectors:
We will start by finding the components of the vectors Ā and B in the x-y plane. Since the magnitude of each vector is 10 units, we can use trigonometry to find the x and y components.
For vector Ā inclined at an angle of 30 degrees, we have:
- x-component = magnitude * cos(angle) = 10 * cos(30) = 8.66025
- y-component = magnitude * sin(angle) = 10 * sin(30) = 5
Similarly, for vector B inclined at an angle of 60 degrees, we have:
- x-component = magnitude * cos(angle) = 10 * cos(60) = 5
- y-component = magnitude * sin(angle) = 10 * sin(60) = 8.66025
Finding the Resultant Vector:
We can find the resultant vector by adding the x and y components of the two vectors.
- x-component of resultant vector = sum of x-components of Ā and B = 8.66025 + 5 = 13.66025
- y-component of resultant vector = sum of y-components of Ā and B = 5 + 8.66025 = 13.66025
To find the magnitude of the resultant vector, we can use the Pythagorean theorem:
magnitude of resultant vector = sqrt((x-component)^2 + (y-component)^2)
= sqrt((13.66025)^2 + (13.66025)^2)
= 19.395 units
Finding the Angle of the Resultant Vector:
We can find the angle of the resultant vector by using the inverse tangent function:
angle of resultant vector = atan(y-component/x-component)
= atan(13.66025/13.66025)
= 45 degrees
Therefore, the resultant vector has a magnitude of 19.395 units and is inclined at an angle of 45 degrees to the x-axis.