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: 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
Question : Assertion (A): The price demand curve is negatively sloped. Reason (R): Inverse relationship between price and demand is stated by the law of demand, holding all other parameters constant.
Option 1: Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Option 2: Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A)
Option 3: Assertion (A) is true but Reason (R) is False
Option 4: Assertion (A) is False but Reason (R) is True
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