Vectors Test- 5 Class 12 Notes | EduRev

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

 Page 1


CBSE TEST PAPER-05 
CLASS - XII MATHEMATICS (Vectors & Three Dimensional Geometry) 
Topic: - Vectors 
1. Is the measure of 1000 cm
3 
is scalar or vector. [1] 
2. Write two different vectors having same direction. [1] 
3.
Find the direction ratios and the direction cosines of the vector 
? ?
2 r i j k = + - 
?
[1] 
4.
Find angle between two vectors    1, 2 . 1 a and b if a b a b = = =
      [1] 
5.
Find a vector in the direction of vector 
?
 2 a i j = - 
?
 that has magnitude 7 units. 
[1] 
6.
If
? ?
 a i j k = + +

?
, 
? ?
 b j k = - 
 find a vector c

 such that .  . 3 a c b and a c × = =
     [4] 
7.
Find the value of ? so that the vectors 
? ? ? ?
2 4  4 8 i j k and i j k ? - + - +
? ?
 are (i) parallel
(ii) perpendicular
[4] 
8. 
Show that 
? ?
( )
1
2 3 6
7
a i j k = + +

? ? ?
( )
? ?
( )
1 1
6 2 3 3 6 2
7 7
b i j k c i j k = + - = - +
 
? ?
[4] 
9.
If 
? ? ? ?
3 2 2 2 4 a i j k b i j k = + + = - +
 
? ?
find 
(i) Magnitude of a b ×
 
 
(ii) A unit vector ?  a and b
 
 to both 
(iii) The cosine and cosine of the angle b w the vectors   a and b
 
[4] 
10.
The vectors 
? ? ? ?
3 and 2 a i x j k b i j yk = + - = - +
 
? ?
 are mutually ? . Given , a b =
 
find 
x and y
[4] 
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