Question

The resultant of two vectors is perpendicular to one of them and has the magnitude 4m. If the sum of the magnitude oftwo vectors is 8m then their respective magntiude are

Answer 1

Answer:

A = 3m

B = 5m

Explanation:

The resultant of two vectors is perpendicular to one of them and has the magnitude 4m. If the sum of the magnitude of  two vectors is 8m then their respective magntiude are

To Simplify

Let say one vector is Ai

and second vector is   BCosαi + BSinαj

A + B = 8m

Resultant = Ai + BCosαi + BSinαj  ⊥ Ai

=> Ai + BCosαi  = 0    

=> BCosα = -A      &   BSinα = 4m

Squaring & adding

B² = A² + (4m)²

=> (8m-A)² = A² + (4m)²

=> 64m² + A² - 16Am = A² + 16m²

=> 48m² =16Am

=> A = 3m

=> B = 5m