A vector of maginitude 3 units is inclined at an angle of 30 degrees to the X-axis and another vector of magnitude of 7 units is inclined at 50 degrees to the X-axis. What is the magnitude of the sum of the vector components. (1) along the X-axis (2) along the Y-axis.
To find the components of the vectors along the X-axis and Y-axis, we can use trigonometry.
Let's start with the vector of magnitude 3 units inclined at 30 degrees to the X-axis.
The X-component of this vector can be found using the formula: X-component = magnitude * cosine(angle)
X-component = 3 * cos(30 degrees)
X-component = 3 * √3 / 2
X-component = 3√3 / 2
The Y-component of this vector can be found using the formula: Y-component = magnitude * sine(angle)
Y-component = 3 * sin(30 degrees)
Y-component = 3 * 1/2
Y-component = 3/2
Now, let's move on to the vector of magnitude 7 units inclined at 50 degrees to the X-axis.
The X-component of this vector can be found using the formula: X-component = magnitude * cosine(angle)
X-component = 7 * cos(50 degrees)
The Y-component of this vector can be found using the formula: Y-component = magnitude * sine(angle)
Y-component = 7 * sin(50 degrees)
The magnitude of the sum of the vector components along the X-axis is the sum of the X-components of both vectors:
Magnitude along X-axis = X-component of vector 1 + X-component of vector 2
Similarly, the magnitude of the sum of the vector components along the Y-axis is the sum of the Y-components of both vectors.