Hello Azhar,
Resultant of two forces P and Q is R
R = P + Q
|R| = sqrt(P^2 + Q^2 + 2PQCosθ)
When Q is doubled new resultant R’ is
R’ = P + 2Q
Since it is perpendicular to P, the dot product of R’ and P is zero
(R’).(P) = 0
(P + 2Q).(P) = 0
P^2 + 2PQCosθ = 0
(Dot product of P and P is P^2 and that of P and 2Q is 2PQCosθ)
Cosθ = -P/(2Q)
R = sqrt(P^2 + Q^2 + 2PQCosθ)
R = sqrt(P^2 + Q^2 + 2PQ*(-P/(2Q))
R = sqrt(P^2 + Q^2 - P^2)
R = Q
Hope this helps.
Question : Directions: P # Q means P is the husband of Q; P + Q means P is the son of Q; P @ Q means P is the brother of Q; P % Q means P is the father of Q; P & Q means P is the mother of Q; P × Q means P is the wife of Q. Which of the following statements is correct regarding the given expression? M × O + N @ Q % R # S
Option 1: M is the brother of R
Option 2: M is the daughter-in-law of R
Option 3: O is the daughter of Q
Option 4: N is the brother of R’s father
Question : Directions: A @ B means A is the husband of B. A & B means A is the mother of B. A # B means A is the wife of B. Which of the following options would mean P is the father-in-law of S?
Option 1: P @ Q & S # R
Option 2: Q @ P & R # S
Option 3: P @ Q & R # S
Option 4: P @ Q & R & S
Question : Directions: There is a family of six persons P, Q, R, S, T and U. They are a Lawyer, Doctor, Teacher, Salesman, Engineer and Manager. There are two married couples in the family. S, the Salesman is married to the lady Teacher. The Doctor is married to the Lawyer. U, the Manager, is the son of Q and brother of T. R, the Lawyer, is the daughter-in-law of P. T is the unmarried Engineer. P is the grandmother of U. Which of the following is one of the married couples?
Option 1: T and R
Option 2: P and S
Option 3: S and Q
Option 4: T and P
Question : Directions: There is a family of six persons P, Q, R, S, T and U. They are a Lawyer, Doctor, Teacher, Salesman, Engineer and Manager. There are two married couples in the family. S, the Salesman is married to the lady Teacher. The Doctor is married to the Lawyer. U, the Manager, is the son of Q and brother of T. R, the Lawyer, is the daughter-in-law of P. T is the unmarried Engineer. P is the grandmother of U. What is the profession of P?
Option 1: Lawyer
Option 2: Engineer
Option 3: Doctor
Option 4: Teacher
Question : Directions: Looking at the picture on the wall, he said "My sister-in-law S's husband Q's son N had a sister R". How is S related to R?
Option 1: Daughter
Option 2: Mother-in-law
Option 3: Daughter-in-law
Option 4: Mother
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