Question

The maximum and minimum magnitude of the resultant of two vectors

Answer 1

Answer:

Minimum can be (a^2+b^2-2ab cos theeta)^1/2

Maximum can be (a^2+b^2+2ab cos theeta)^1/2

Answer 2

Answer:

The resultant of two vector is minimum when both vectors are equal and in opposite direction i.e. the angle between the vector is 180 degrees.

Explanation:

The magnitude of resultant R of two vectors A and B is given by;

R² = A² + B² + 2 A B Cos ( A, B ); where

R = magnitude of the resultant R =| R |,

A = magnitude of the vector A = | A |

B = magnitude of vector B = | B |

( A, B ) = Angle between vectors A, and B

R is maximum when Cos ( A, B) = +1 ie angle between vectors A and B is zero ie vectors A and B are parallel to each other.

Resultant is maximum when the two vectors are parallel to each other.-----

The resultant of two vector is minimum when both vectors are equal and in opposite direction i.e. the angle between the vector is 180 degrees.

Therefore they cancel each other out, so the magnitude of the resultant vector is zero---:-) :-) :-) -:-) :-) ---