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# Vectors Test- 5 Class 12 Notes | EduRev

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

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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. 
2. Write two different vectors having same direction. 
3.
Find the direction ratios and the direction cosines of the vector
? ?
2 r i j k = + - 
?

4.
Find angle between two vectors    1, 2 . 1 a and b if a b a b = = =
      
5.
Find a vector in the direction of vector
?
2 a i j = - 
?
that has magnitude 7 units.

6.
If
? ?
a i j k = + +

?
,
? ?
b j k = - 
find a vector c

such that .  . 3 a c b and a c × = =
     
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

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 = + - = - +
 
? ?

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
 

10.
The vectors
? ? ? ?
3 and 2 a i x j k b i j yk = + - = - +
 
? ?
are mutually ? . Given , a b =
 
find
x and y

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