Question

Physics:-

Class 11

The maximum and minimum resultant of 2 vectors is 10 and 4 . The ratio of their magnitude is ​

Answer 1

Answer:

7 : 3

Explanation:

Maximum resultant of n vectors is found when they are all in same direction.

That is their algebraic sum in same direction.

For the given two vectors(say A and B):

Maximum resultant = A + B

Minimum resultant of two vectors is found when they are all in opposite direction.

That is their algebraic sum in opposite direction.

For the given two vectors(say A and B):

Minimum resultant = A + (-B) = A - B

In the given question :

Max. resultant: A + B = 10

Min. resulrant: A - B = 4

Adding both,

=> (A + B) + (A - B) = 10 + 4

=> 2A = 14

=> A = 7

Therefore, A + B = 10 => 7 + B = 10

Hence, B = 3

Therefore, required ratio is A/B = 7:3

____Proof(max result)______

Resultant = √A² + B² + 2ABcos∅

For ∅ = 0° (vectors are in same direction)

Result = √A² + B² + 2ABcos0°

Result = √A² + B² + 2AB = A + B

_____Proof(min result)_______

Resultant = √A² + B² + 2ABcos∅

For ∅ = 180° (vectors in oppo. direction)

Result = √A² + B² + 2ABcos180°

Result = √A² + B² - 2AB = A - B