Question

the ratio of maximum and minimum magnitudes of the resultant of 2 vectors a and b is3:1.now

Answer 1

Answer:

Solution:-

angle b/w them is 0. Resultant is min when angle is 180.

$∴   ∣∣∣∣a−b∣∣∣∣∣∣∣∣a+b∣∣∣∣$

=a2+b2−2aba2+b2+2ab=13

⇒a2+b2+2ab=9a2+9b2−18ab

⇒8a2+8b2−20ab=0

⇒2a2+2b2−5ab=0

Let a=x.b            

⇒2x2b2+2b2

Answer 2

• The maximum resultant is produced when they act in the same direction.

a + b = 3

• The minimum resultant is produced when they act on opposite directions.

a - b = 1

From the question,

(a + b)/(a - b) = 3/1

3a - 3b = a + b

3a - a = b + 3b

2a = 4b

a = 2b