Solution- Vectors Test-5 Class 12 Notes | EduRev

Created by: Arshdeep Kaur

Class 12 : Solution- Vectors Test-5 Class 12 Notes | EduRev

 Page 1


CBSE TEST PAPER-05 
CLASS - XII MATHEMATICS (Vectors & Three Dimensional Geometry) 
Topic: - Vectors  [ANSWERS] 
Ans1.  Scalar 
Ans2. 
? ?
1 3 5 a i j k = + +

?
? ?
? ?
( )
2 4 6
2 2 3
2
b i j k
b i j k
b a
= + +
= + +
=

?

?
 
Ans3. .    1,1, 2 D R of r are - 
1 1 4 6
1 1 2
.   , ,
6 6 6
r
D C of r are
= + + =
- 

Ans4. 
.
cos
a b
a b
? =
 
 
( )( )
1 1
cos
1 2 2
cos cos
3 3
?
p p
? ?
= =
= ? =
Ans5. 
?
a
a
a
=


?
( )
2
5
i j - =
?
Vector having magnitude equal to 7 and in the direction of a

 is 
?
?
?
( )
2
7 7
5
7
2
5
i j
a
i j
? ?
- =
? ?
? ?
? ?
= - ?
?
Page 2


CBSE TEST PAPER-05 
CLASS - XII MATHEMATICS (Vectors & Three Dimensional Geometry) 
Topic: - Vectors  [ANSWERS] 
Ans1.  Scalar 
Ans2. 
? ?
1 3 5 a i j k = + +

?
? ?
? ?
( )
2 4 6
2 2 3
2
b i j k
b i j k
b a
= + +
= + +
=

?

?
 
Ans3. .    1,1, 2 D R of r are - 
1 1 4 6
1 1 2
.   , ,
6 6 6
r
D C of r are
= + + =
- 

Ans4. 
.
cos
a b
a b
? =
 
 
( )( )
1 1
cos
1 2 2
cos cos
3 3
?
p p
? ?
= =
= ? =
Ans5. 
?
a
a
a
=


?
( )
2
5
i j - =
?
Vector having magnitude equal to 7 and in the direction of a

 is 
?
?
?
( )
2
7 7
5
7
2
5
i j
a
i j
? ?
- =
? ?
? ?
? ?
= - ?
?
Ans6. 
? ?
a i j k = + +

?
? ?
? ?
1 2 3
 
b j k
Let c c i c j c k
= - = + +


?
? ?
1 2 3
1 1 1
a c b
i j k
b
c c c
× =
=
  
?

( )
?
( )
?
( )
? ?
3 2 3 1 2 1
3 2
.
0
i c c j c c k c c j k
c c
- - - + - = - - =
?
3 2
3 1
( )
1 ( )
c c i
c c ii
= - - - - - - - - - + = - - - - - 2 1
1 ( )
 . 3
c c iii
also a c
- = - - - - - - =

1 2 3
3 ( )
on solving equaiton (i) (ii) (iii) and (iv)
c c c iv + + = - - - - ?
1 2 3
2
5 2
, , 
3 3
3
2
5 2
j .
3 3
3
c c c
c i k
= = =
= + +

? ?
Ans7. (i) Given vectors are parallel 
? ?
2 4 1 0
4 8
2
i j k
if
?
?
- =
- =
?
(ii)    For ?
 
? ?
( )
? ?
( )
4 8 . 2 4 0
8 32 0
40
i j k i j k ?
?
?
- + - + =
+ + =
= - ? ?
Ans8. 1 a =

1
1
b
c
=
=


Page 3


CBSE TEST PAPER-05 
CLASS - XII MATHEMATICS (Vectors & Three Dimensional Geometry) 
Topic: - Vectors  [ANSWERS] 
Ans1.  Scalar 
Ans2. 
? ?
1 3 5 a i j k = + +

?
? ?
? ?
( )
2 4 6
2 2 3
2
b i j k
b i j k
b a
= + +
= + +
=

?

?
 
Ans3. .    1,1, 2 D R of r are - 
1 1 4 6
1 1 2
.   , ,
6 6 6
r
D C of r are
= + + =
- 

Ans4. 
.
cos
a b
a b
? =
 
 
( )( )
1 1
cos
1 2 2
cos cos
3 3
?
p p
? ?
= =
= ? =
Ans5. 
?
a
a
a
=


?
( )
2
5
i j - =
?
Vector having magnitude equal to 7 and in the direction of a

 is 
?
?
?
( )
2
7 7
5
7
2
5
i j
a
i j
? ?
- =
? ?
? ?
? ?
= - ?
?
Ans6. 
? ?
a i j k = + +

?
? ?
? ?
1 2 3
 
b j k
Let c c i c j c k
= - = + +


?
? ?
1 2 3
1 1 1
a c b
i j k
b
c c c
× =
=
  
?

( )
?
( )
?
( )
? ?
3 2 3 1 2 1
3 2
.
0
i c c j c c k c c j k
c c
- - - + - = - - =
?
3 2
3 1
( )
1 ( )
c c i
c c ii
= - - - - - - - - - + = - - - - - 2 1
1 ( )
 . 3
c c iii
also a c
- = - - - - - - =

1 2 3
3 ( )
on solving equaiton (i) (ii) (iii) and (iv)
c c c iv + + = - - - - ?
1 2 3
2
5 2
, , 
3 3
3
2
5 2
j .
3 3
3
c c c
c i k
= = =
= + +

? ?
Ans7. (i) Given vectors are parallel 
? ?
2 4 1 0
4 8
2
i j k
if
?
?
- =
- =
?
(ii)    For ?
 
? ?
( )
? ?
( )
4 8 . 2 4 0
8 32 0
40
i j k i j k ?
?
?
- + - + =
+ + =
= - ? ?
Ans8. 1 a =

1
1
b
c
=
=


Hence they are unit vectors 
. 0
. 0
a b
b c
=
=
 

. 0
,   
c a
a b b c and c a
=
? ? ?

     
So they are ? to each other.
Ans9. (i)
? ?
3 1 2
2 2 4
i j k
a b × =
- ?
 
? ?
8 8 8
8 3
i j k
a b
= - - × =
?
 
(ii) 
a b
a b
×
=
+
 
 
? ?
8 8 8
8 3
i j k - - =
?
(iii) . 12 a b =
 
14
24
a
b
=
=


 
.
cos
a b
a b
? =
 
 
12 3
14. 24 7
sin
a b
Also
a b
?
= =
+
=
 
 
8 3
14 24
2
7
=
=
Ans10. . 0 a b a b
?
= ?
?
   
?
( )
6 (1) y x
a b Given
- = - - - - - - - - =
 
2 2 2 2 2
2 2
3 1 2 1
5
x y
y x
+ + = + +
- =
( )( )
( )
5
6 5
y x y x
y x
- + =
- =
5
6
31 41
,
12 12
y x
x y
- =
- = =
Read More
Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Content Category

Related Searches

practice quizzes

,

Important questions

,

Sample Paper

,

pdf

,

video lectures

,

Objective type Questions

,

Semester Notes

,

mock tests for examination

,

Exam

,

shortcuts and tricks

,

ppt

,

past year papers

,

Summary

,

Extra Questions

,

Free

,

Solution- Vectors Test-5 Class 12 Notes | EduRev

,

study material

,

Solution- Vectors Test-5 Class 12 Notes | EduRev

,

Viva Questions

,

Previous Year Questions with Solutions

,

Solution- Vectors Test-5 Class 12 Notes | EduRev

,

MCQs

;