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Question

The sum of two forces P and Q is R such that R=P. The angle θ (in degrees) that the resultant of 2P and Q will make with Q is, ______.


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Solution

Step 1: Given Data

Sum of the two forces, P+Q=R

R=P

the angle between resultant of 2P+Q and Q​ is θ

the angle between resultant of R and Q​ is ϕ

Step 2: Formula Used

Sum of the angles of a triangle=90°

Step 3: Calculate the value of θ

Let BOA=ϕ +
ln ΔOBE

BE=OB

BEO=BOE=θ-ϕ

ln ΔOBE

BEO+BOE+EBO=180

(θϕ)+2ϕ+(θϕ)=180

2θ+2ϕ2ϕ=180

2θ=180

θ=90

So, vector 2P+Q will make 90 with Q.

Hence, the angle θ (in degrees) that the resultant of 2P and Q will make with Q is, 90°.


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