Vectors & Three Dimensional Geometry Test - 1 Notes - Class 12

Class 12: Vectors & Three Dimensional Geometry Test - 1 Notes - Class 12

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CBSE TEST PAPER-01 
CLASS - XII MATHEMATICS (Vectors & Three Dimensional Geometry) 
Topic: - Vectors 
1. Is the measure of 5 seconds is scalar or vector? [1] 
2. Find the sum of the vectors.
? ?
2 ,     2 4 5  6 7 a i j k b i j k c i j k = - + = - + + = - -         
?
[1] 
3. Find the direction ratios and the direction cosines of the vector
? ?
 2 7 3 r i j k = - - 
?
[1] 
4.
Find the angle between vectors    3, 2     . 6 a and b if a b a b = = =
     
[1] 
5. 
Vectors   a and b
 
 be such that 
2
3,  ,
3
a and b = =
 
then a b ×
 
 is a unit vector. 
Find angle between  a and b
 
. 
[1] 
6. Find the unit vector in the direction of the sum of the vectors
? ? ? ?
2 2 5 ,  2 3 a i j k b i j k = + - = + +
 
? ?
[4] 
7.
Show that the points 
? ?
( )
? ?
( )
? ?
( )
2 , 3 5 , 3 4 4 A i j k B i j k C i j k - + - - - - ? ? ?
 are the
vertices of right angled triangle. 
[4] 
8.
Show that the points 
? ?
( )
? ?
( )
?
( )
2 3 5 , 2 3 7 A i j k B i j k and C i k - + + + + - ? ? ?
 are
collinear. 
[4] 
9.
If , , a b c
  
are unit vector such that 0 a b c + + =
  
find the value of . . . a b b c c a + +
     
[4] 
10.
If 
? ? ? ? ?
2 2 3 ,  2  , 3 a i j k b i j k c i j = + + = - + + = +
  
? ? ?
are such that   a b is to c ? + ?
  
 is 
then find the value of ? .
[4] 
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