wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The resultant of P and Q is R. If Q is doubled, R is also doubled and if Q is reversed, R is again doubled. Then, P2:Q2:R2 given by

A
2:2:3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
3:2:2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
2:3:2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
2:3:1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 2:3:2
Given, R=P+Q
|R|2=|P|2+|Q|2+2|P||Q|cosθ...(1)
Now 2R=P+2Q
4|R|2=|P|2+4|Q|2+4|P||Q|cosθ...(2)
Now 2R=PQ
4|R|2=|P|2+|Q|22|P||Q|cosθ...(3)
Add (1) and (3)
5|R|2=2|P|2+2|Q|2...(4)
Now multiply equation (3) with 2 and then add it with (2)
12|R|2=3|P|2+6|Q|2
4|R|2=|P|2+2|Q|2...(5)
Now equation (4)-(5)
|R|2=|P|2
Now from equation (4)
5|R|2=2|R|2+2|Q|2
|Q|2=32|R|2
Therefore, |P|2:|Q|2:|R|2=|R|2:32|R|2:|R|2
=2:3:2

flag
Suggest Corrections
thumbs-up
75
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Vector Addition
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon