Question

If vec a+vec b+vec c=0. The angle between vec a and vec b and that between vec b and vec c are 150^(@) and 120^(@) respectively. Then the magnitude of vectors.vec a vec b and vec c are in ratio of

Answer 1

Answer:

Explanation:

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We have,

a+b=c ……………………(1)

Also,

|a|+|b|=|c| …………(2)

Square the equation, (1), we get,

(a+b).(a+b)=c.c

Implies,

|a|2+|b|2|+2(a.b)=|c|2 ……….(3)

From (2), we can get,

|a|2+|b|2|+2|a||b|=|c|2 ………(4)

Since the RHS’s of (3) and (4) are same, we can equate them, we get,

|a|2+|b|2|+2(a.b)=|a|2+|b|2|+2|a||b|

Implies,

a.b=|a||b|

Dot Product of 2 vectors is the product of absolute values of the vectors with the cosine of angle between them. So,

|a||b|cosx=|a||b|

Here, x is the angle between a and b.

So,...

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Punyasloka Sahoo

Punyasloka Sahoo, former Summer Intern at Indian Institute of Technology, Bhubaneswar (2019)

Updated May 16, 2019 · Author has 291 answers and 375.1k answer views

Simple, the angle between the 2 vectors is 0 degree.

First a+b= c

=>(a^2+b^2+2abcos(theta))^(1/2)=| c|

where theta is the angle between a and b.

Again a+b=c

=> (a+b)^2=c^2=| c |^2=a^2+b^2+2abcos(theta)

=>a^2+b^2+2ab=a^2+b^2+2abcos(theta)

((a+b)^2=a^2+b^2+2ab)

=>2abcos(theta)=2ab

=> cos(theta)=1

=>theta=0 degree