The resultant of vector P n …
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The resultant of vector P n Q is vector R. If vector Q is doubled, vector R is doubled. When vector Q is reversed, vector R is again doubled. Find P:Q:R.
Posted by Aadya Singh 4 years, 7 months ago
- 3 answers
Sharma Sadul? 4 years, 7 months ago
Let take the angle between P and Q is θ.
The force expression according to given conditions are given as,
P2+Q2+2PQcosθ=R2 (1)
When Q is doubled,
P2+4Q2+4PQcosθ=4R2 (2)
When Q is reversed,
P2+Q2−2PQcosθ=4R2 (3)
Subtracting equation (3) from equation (1), we get
4PQcosθ=−3R2
PQcosθ=4−3R2 (4)
Substituting the value from equation (4) to equation (1), (2) and (3), we get
P2+Q2=25R2
P2+4Q2=7R2
P2+Q2=25R2
Simplify the above equations, we get
P2=R2
Q2=23R2
Thus, the ratio is P:Q:R=√2:√3:√2.
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Aadya Singh 4 years, 7 months ago
0Thank You