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# Solution- Vectors Test-4 Class 12 Notes | EduRev

## Class 12: Solution- Vectors Test-4 Class 12 Notes | EduRev

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CBSE TEST PAPER-04
CLASS - XII MATHEMATICS (Vectors & Three Dimensional Geometry)
Ans1.  Scalar
Ans2. ( ) ( ) ( )
2 2 2
2 7 3 b = + - + - 
4 49 9
62
= + +
=
Ans3. D.R of   1,2, 1 r are - 
1 4 1 6 r = + + =

D.C of
1 2 1
, ,
6 6 6
r are
- 
Ans4. 1 a =

( ) ( )
2
. 8
1 8
x a x a
x
- + =
- =
   

2
2
9
3
x
x
=
=


Ans5.
( ) ( )
. . L H S a b a b = - × +
   
0 0
a a a b b a b b
a b a b
= × + × - × - ×
= + × + × -        
   
( )
0
2
a b
a b
a b b a
?
× =
= ×
?
× = - × ?
?
 
 
?
   
Ans6. 0 a b c + + =
  
( )
. 0
. . . 0
a a b c
a a a b a c
+ + =
+ + =
   
    
Page 2

CBSE TEST PAPER-04
CLASS - XII MATHEMATICS (Vectors & Three Dimensional Geometry)
Ans1.  Scalar
Ans2. ( ) ( ) ( )
2 2 2
2 7 3 b = + - + - 
4 49 9
62
= + +
=
Ans3. D.R of   1,2, 1 r are - 
1 4 1 6 r = + + =

D.C of
1 2 1
, ,
6 6 6
r are
- 
Ans4. 1 a =

( ) ( )
2
. 8
1 8
x a x a
x
- + =
- =
   

2
2
9
3
x
x
=
=


Ans5.
( ) ( )
. . L H S a b a b = - × +
   
0 0
a a a b b a b b
a b a b
= × + × - × - ×
= + × + × -        
   
( )
0
2
a b
a b
a b b a
?
× =
= ×
?
× = - × ?
?
 
 
?
   
Ans6. 0 a b c + + =
  
( )
. 0
. . . 0
a a b c
a a a b a c
+ + =
+ + =
   
    
2
. .
. . 1 ( )
a b a c a
a b a c i
+ = - + = - - - - - - - -     
   
. . 16 ( )
. . 4 ( )
b a b c ii
a c b c iii
+ = - - - - - - + = - - - - - -   
 
( )
2 . . . 21
21
2
a b b c a c
µ
+ + = - - =
    
Ans7.
1 1
|| Let to ß ?a ß a
?
=
?
   
?
?
( )
?
1
3
3
i j
i j
ß ?
? ?
= - = - 
?
?
? ?
( )
?
( )
2 1

2 3 3 i j k i j
ß ß ß
? ?
= - = + - - -   
? ?
( ) ( )
? ?
2 2
2 3 1 3
. 0
i j k ? ?
a ß ß a
= - + + - ?
= ?
?
?
  
?
( ) ( ) 3 2 3 1 0
1
2
? ?
?
- - + =
=
?
? ?
1
2
3 1
2 2
1 3
3
2 2
i j
i j k
ß
ß
= - = + - 
?

?
Ans8. 0 a b c + + =
  
a b c + = -   
( ) ( ) ( )
( ) ( )
. .
. .
a b c c c
a b a b c c
+ - = - - + + =
    
    
2 2 2
2
49 9 25 15
.
2 2
a ab b c
a b
+ + =
- - = =
   
 
Page 3

CBSE TEST PAPER-04
CLASS - XII MATHEMATICS (Vectors & Three Dimensional Geometry)
Ans1.  Scalar
Ans2. ( ) ( ) ( )
2 2 2
2 7 3 b = + - + - 
4 49 9
62
= + +
=
Ans3. D.R of   1,2, 1 r are - 
1 4 1 6 r = + + =

D.C of
1 2 1
, ,
6 6 6
r are
- 
Ans4. 1 a =

( ) ( )
2
. 8
1 8
x a x a
x
- + =
- =
   

2
2
9
3
x
x
=
=


Ans5.
( ) ( )
. . L H S a b a b = - × +
   
0 0
a a a b b a b b
a b a b
= × + × - × - ×
= + × + × -        
   
( )
0
2
a b
a b
a b b a
?
× =
= ×
?
× = - × ?
?
 
 
?
   
Ans6. 0 a b c + + =
  
( )
. 0
. . . 0
a a b c
a a a b a c
+ + =
+ + =
   
    
2
. .
. . 1 ( )
a b a c a
a b a c i
+ = - + = - - - - - - - -     
   
. . 16 ( )
. . 4 ( )
b a b c ii
a c b c iii
+ = - - - - - - + = - - - - - -   
 
( )
2 . . . 21
21
2
a b b c a c
µ
+ + = - - =
    
Ans7.
1 1
|| Let to ß ?a ß a
?
=
?
   
?
?
( )
?
1
3
3
i j
i j
ß ?
? ?
= - = - 
?
?
? ?
( )
?
( )
2 1

2 3 3 i j k i j
ß ß ß
? ?
= - = + - - -   
? ?
( ) ( )
? ?
2 2
2 3 1 3
. 0
i j k ? ?
a ß ß a
= - + + - ?
= ?
?
?
  
?
( ) ( ) 3 2 3 1 0
1
2
? ?
?
- - + =
=
?
? ?
1
2
3 1
2 2
1 3
3
2 2
i j
i j k
ß
ß
= - = + - 
?

?
Ans8. 0 a b c + + =
  
a b c + = -   
( ) ( ) ( )
( ) ( )
. .
. .
a b c c c
a b a b c c
+ - = - - + + =
    
    
2 2 2
2
49 9 25 15
.
2 2
a ab b c
a b
+ + =
- - = =
   
 
.
cos
1
2
60
a b
a b
?
?
=
=
=
 
 
Ans9.
? ?
3 1 2
1 3 4
i j k
a b × = - - ?
 
? ?
( ) ( ) ( )
2 2 2
2 14 10
.
2 14 10 10 3
i j k
req area a b
= - - - = ×
= - + - + - =
?
 
Ans10. ( ) ( )
?
( )
?
1 2 2 3 4 0 PQ i j k = - - + - - + - - 
?
? ?
3 5 4
3, 5, 4
i j k
DR are
= - - - - - - ?
9 25 16
3 5 4
. , ,
50 50 50
PQ
D C are
= + +
- - - 
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