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If resultant of two vectors a and b shown in the figure is √7b. The value of b/a is?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

If the resultant of two vectors a and b shown in the figure is √7b. The value of b/a is 1/2. Steps to find the value of b/a is:

Step 1: It is given that:

The angle between a and b, θ = 600

Resultant of a and b is √7b

Step 2: Formula to calculate the results of A and B:

Resultant of A and B is written as,

R2 = A2 + B2 + 2AB cosθ

Step 3: In the equation above, by replacing the provided numbers, we obtain:

The fact that the product of a and b is √7b

R2 = A2 + B2 + 2AB cosθ

Substituting the given values in the above equation we get:

(√7b)2 = a2 + b2 + 2ab cos 600

7b2 = a2 + b2 + 2ab (½) [As cos 600 = ½]

6b2 = a2 + ab

a2 + ab – 6b2 = 0

Step 4: Finding the values of a and b by solving the equation:

The middle term is divided, and we obtain:

a2 + 3ab – 2ab – 6b2 = 0

a (a + 3b) – 2b (a + 3b) = 0

(a – 2b) (a + 3b) = 0

a = 2b or a = -3b

Given that the angle of the two vectors in the illustration is 600, if we take into account the negative value, the b direction will be the opposite and the angle will change. Thus, we only take into account positive values. Taking into account a’s positive value, we obtain the:

a = 2b

b/a = ½

Hence, the value of b/a is ½.

Summary:

If resultant of two vectors a and b shown in the figure is √7b. The value of b/a is?

If resultant of two vectors a and b shown in the figure is √7b. The value of b/a is ½.

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