How does the resultant of two vectors change as the angle between the two vectors increase?
To understand how the resultant of two vectors changes as the angle between them increases, we need to consider vector addition.
When two vectors are added, their resultant is found by drawing them as arrows, placing the tail of one vector at the tip of the other, and then drawing the resultant vector from the tail of the first vector to the tip of the second vector. The magnitude and direction of the resultant vector depend on the magnitudes and directions of the individual vectors.
Now, let's consider the angle between two vectors. If the angle between the vectors is 0 degrees (or they are parallel), the two vectors are in the same direction, and their resultant will have the maximum magnitude. As the angle between the vectors increases, the magnitude of the resultant vector decreases.
When the angle between the vectors is 90 degrees, the vectors are perpendicular to each other. In this case, the magnitude of the resultant vector is given by the Pythagorean theorem, i.e., the square root of the sum of the squares of the magnitudes of the individual vectors.
As the angle between the vectors continues to increase beyond 90 degrees, the magnitude of the resultant vector continues to decrease. When the angle between the vectors is 180 degrees (or they are opposite in direction), the resultant will have the minimum magnitude, which is the difference between the magnitudes of the two vectors.
In summary, as the angle between two vectors increases from 0 degrees to 180 degrees, the magnitude of the resultant vector decreases. At 0 degrees, the resultant vector has the maximum magnitude, while at 180 degrees, the resultant vector has the minimum magnitude.