Question

The maximum resultant of the 2 vectors is 26 units and the minimum resultant is 16 units. The magnitudes of the 2 vectors are:
(A) 20, 6
(B) 13,13
(C) 21,5
(D) 10,16

Answer 1

Hint: The maximum resultant of 2 vectors is when the angle between them is 0 and the minimum resultant is when the angle between them is 180. Substitute the angle between them and we get two equations for max and min respectively. Solve the equations simultaneously to find the magnitude of the vectors.

Complete step-by-step solution
Let the 2 vectors be A and B, the resultant of 2 vectors is given by
 \[{R^2} = {A^2} + {B^2} + 2AB\cos \theta \]
The maximum value of the resultant is when the angle between 2 vectors is 0 or the \[\cos \theta \] is 1. This will give the equation
 \[R = A + B\]
Similarly, the minimum value of the resultant is when the angle between them is 180 or cos theta is -1, this will give:
 \[R = A - B\]
Solving these 2 equations to find the value of A and B, we get
 \[A = 21\]
 \[B = 5\]

Therefore, the correct option is option C

Note
When the 2 vectors are perpendicular to each other, the angle between them is 90 and the cos theta is 0. This will form an equation which is similar to the Pythagoras equation for a right-angled triangle