Question

What are the first two steps for finding the magnitude of the resultant vector?

Answer 1

In the analytical method,

1. Resolve the vectors into the perpendicular components of the Cartesian coordinates.
2. Calculate the magnitude of the resultant vector using the Pythagoras theorem.

Explanation:

• There are two methods to find the magnitude of the resultant vector.
• One is the geometrical method and the other one is the analytical method.
• In the geometrical method, all the vectors are connected the head to tail with the appropriate magnitude and the resultant vector is obtained by joining the initial point and the final point by a vector in the reverse direction. The magnitude of the resultant vector is given by the length of the line.
• In the analytical method, all the vectors are resolved into the perpendicular components.
• Using Pythagoras theorem, the magnitude of the resultant vector can be obtained
• If A and B are the two vectors forming an angle ∅ between them, then the magnitude of the resultant vector is given by the formula

`R=\sqrt{A^(2)+B^(2)+2ABcos\phi}`