1 ) Which pair of following forces will never give resultant of 2N ?
A ) 2 N and 2 N , B ) 1 N and 1 N ,
C ) 1 N and 3 N , D ) 1 N and 4 N ,
Correct Answer : -
Solution : -
We have a simple trick to check whether a number is resultant or not : -
| A – B | <= R <= | A + B | ,
So , first we put the values of option A ,
| 2 – 2 | <= R <= | 2 + 2 | ,
0 <= R <= 4 ,
So all the values in between 0 and 4 , also including 0 and 4 are resultants . So 2 is resultant . This option is incorrect .
Now , we put the values of option D ,
| 1 – 4 | <= R <= | 1 + 4 | ,
| – 3 | <= R <= | 5 | ,
Now values are under mode , so – ve sign will change into + ve .
3 <= R <= 5 ,
So all the values in between 3 and 5 , also including 3 and 5 are resultants . So 2 is not resultant . So , D option is correct .
2 ) Vector product : -
i x j = k , j x k = i , k x i = j .
3 ) Angular momentum is axial vector .
4 ) | A • B | = | A x B | : -
A ) 0 degree , B ) 45 degree ,
C ) 90 degree , D ) None of these ,
Correct Answer : - B ) 45 degree ,
5 ) | A + B | = | A - B | : -
A ) 0 degree , B ) 45 degree ,
C ) 90 degree , D ) None of these ,
Correct Answer : - C ) 90 degree ,
6 ) Find angle between these two vectors - 2i + 3j + k and i + 2j – 4k is : -
A ) 0 degree , B ) 90 degree ,
C ) 180 degree , D ) None of these ,
Correct Answer : - B ) 90 degree ,
Solution : -
We have formula : -
Cos θ = A • B / ( | A | | B | ) . . . . . . . . . . eq. 1
∴ A = - 2i + 3j + k and B = i + 2j – 4k ,
∴ A •B = ( - 2 ) ( 1 ) + ( 2 ) ( 3 ) + ( - 4 ) ( 1 ) = 0 .
∴ | A | = √ {( - 2 ) ^ 2 + ( 2 ) ^ 2 + ( - 4 ) ^ 2} = √ 14 .
∴ | B | = √ {( 1 ) ^ 2 + ( 2 ) ^ 2 + ( - 4 ) ^ 2} = √ 21 .
So , put these all values in eq. 1 ;
Cos θ = 0 / ( √ 14 • √ 21 ) ,
Cos θ = 0 ,
So , θ = 90 ° , Answer .
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