1.

EFGH is a rhombus such that the angle EFG is 60^(@). The magnitude of vectorsbar(FH)and {m bar(EG)} are equal where m is a scalar. What is the value of m?

Answer»

3
1.5
`sqrt(2)`
`sqrt(3)`

Solution :
RHOMBUS EFGH, `angle EFG=60^(@)`
`angleEFG=30^(@)=angleHFG`
From parallelogram of FORCES
`vec(FE)+vec(FG)=vec(FG)`
Given `|vec(FE)|+|vec(FG)|=a`(say)
`:.vec(FH)=2. (sqrt(3))/(2)vec(a)=sqrt(3)vec(a)`
`vec(EG)=vec(EF)+vec(EH)`
`=a sin 30^(@)+a sin30^(@)=a. (1)/(2) + a. (1)/(2)=a`
Thus, `(vec(FH))/(vec(EG))=(sqrt(3)a)/(a)=sqrt(3)`
So, `vec(FH)=sqrt(3) vec(EG)`
`rArr m=sqrt(3)`


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