Question

A vector of magnitude 20 is added to a vector of magnitude 25. The magnitude of this sum might be :
(A) zero
(B) 3
(C) 12
(D) 47

Answer 1

Given:

|a | = 20

|b| = 25

★SOLUTION★

As, the vectors are added Hence,

|R|=√(a²+b²+2abcosθ)

⇒R = √[(20)²+(25)²+2(20)(25)(cosθ)]

⇒R =√[400+625+1000cosθ] = √[1025+1000cosθ]

∴ R = 5√[41+40cosθ]

________________________________

Now, as, –1 ≤ cosθ ≤ 1

⇒Rmin= 5√(41–40) = 5 units

and,

⇒Rmax= 5√(41+40) =5(9) = 45 units

[Notice that Rmax= A+B, and Rmin= |A–B|]

Therefore, the Magnitude of the sum of the two vectors must lie between Maximum and Minimum value.

ie, ( Rmin ≤ R ≤ Rmax)

As, third option satisfies this condition, therefore, the correct answer is (C) 12 units.