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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
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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.