The resultant of P vector and Q vector is R vector . If Q vector is
doubled, R vector is doubled; when Q is reversed, R vector
is again doubled. Find P: Q: R.
Answers
Answer:
Let take the angle between P and Q is θ.
The force expression according to given conditions are given as,
P
2
+Q
2
+2PQcosθ=R
2
(1)
When Q is doubled,
P
2
+4Q
2
+4PQcosθ=4R
2
(2)
When Q is reversed,
P
2
+Q
2
−2PQcosθ=4R
2
(3)
Subtracting equation (3) from equation (1), we get
4PQcosθ=−3R
2
PQcosθ=
4
−3
R
2
(4)
Substituting the value from equation (4) to equation (1), (2) and (3), we get
P
2
+Q
2
=
2
5
R
2
P
2
+4Q
2
=7R
2
P
2
+Q
2
=
2
5
R
2
Simplify the above equations, we get
P
2
=R
2
Q
2
=
2
3
R
2
Thus, the ratio is P:Q:R=
2
:
3
:
2
.
Explanation: