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 .
