- #1

Shahab Mirza

- 28

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Question is regarding Scalars and Vectors Article.

Q: One of the two forces is double the other and their resultant is equal to the greater force . The angle between them is ?

Ans : Its answer is cos^-1 (-1/4)

My solution :

The formula for Cosine law is

R= √A

Our teacher told that when talking about force we can write :

F= √F1

F= √F1+F2+2F²cos theta

F=√1+cos theta

But, what I did to solve problem is this below :-

1: I plugged in values . A = F1 , B = 2F , Resultant "R" = 2f

2: I got this equation :

= 2F = √F1² + 2F² +2F(2F) cos theta

= 2F= √F²(cancel) + 2F²(cancel) + 4F² cos theta : F² F² cancel each other

= 2F = √2(cancel)+4(cancel)F² cos theta : 2 and 4 are divided by 2 and cos theta shifts

= F/2F²= √ 1+ cos theta

= 1/4= √1 + cos theta

= cos ^-1 (-1/4)

But I know the way solved is not it is meant to be solved because I am in Pre- Medical and i have less knowledge of mathematics , so Kindly tell me how to deal with such numericals and please solve it and tell me shortest route to solve it . thanks in advance

Q: One of the two forces is double the other and their resultant is equal to the greater force . The angle between them is ?

Ans : Its answer is cos^-1 (-1/4)

My solution :

The formula for Cosine law is

R= √A

**²**+B² +2ABcos thetaOur teacher told that when talking about force we can write :

F= √F1

**+ F2²+F1²X F2² cos theta****²**F= √F1+F2+2F²cos theta

F=√1+cos theta

But, what I did to solve problem is this below :-

1: I plugged in values . A = F1 , B = 2F , Resultant "R" = 2f

2: I got this equation :

= 2F = √F1² + 2F² +2F(2F) cos theta

= 2F= √F²(cancel) + 2F²(cancel) + 4F² cos theta : F² F² cancel each other

= 2F = √2(cancel)+4(cancel)F² cos theta : 2 and 4 are divided by 2 and cos theta shifts

= F/2F²= √ 1+ cos theta

= 1/4= √1 + cos theta

= cos ^-1 (-1/4)

But I know the way solved is not it is meant to be solved because I am in Pre- Medical and i have less knowledge of mathematics , so Kindly tell me how to deal with such numericals and please solve it and tell me shortest route to solve it . thanks in advance

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