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# Vectors & Three Dimensional Geometry Test - 2 Class 12 Notes | EduRev

## Class 12: Vectors & Three Dimensional Geometry Test - 2 Class 12 Notes | EduRev

The document Vectors & Three Dimensional Geometry Test - 2 Class 12 Notes | EduRev is a part of Class 12 category.
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CBSE TEST PAPER-02
CLASS - XII MATHEMATICS (Vectors & Three Dimensional Geometry)
Topic: - Vectors
1. Is the measure of 10 Newton is scalar or vector. [1]
2. Write two different vectors having same magnitude. [1]
3.
Find the direction ratios and the direction cosines of the vector
? ?
r i j k = + +

?
[1]
4.
Find 2, 3  . 4 a b if a b and a b - = = =
     
[1]
5.
If
? ? ?
4 3 2 3 2 2 a i j k b i k find b a = + + = + ×
   
? ?
[1]
6.
Consider two point P and Q with position vectors 3 2  OP a b and OQ a b = - = +
      
. Find the positions vector of a point R which divides the line joining P and Q
in the ratio 2:1 (i) internally (ii) externally.
[4]
7. Show that the points A, B, C with position vectors
2 3 5 , 2 3  7 a b c a b c and a c - + + + + -        
respectively are collinear.
[4]
8. Find a unit vector ? to each of the vectors
( ) ( )
? ? ? ?
, 2 3 a b and a b where a i j k b i j k + - = + + = + +
     
? ?
[4]
9.
The scalar product of the vector
? ?
i j k + +
?
with a unit vector along the sum of
vectors
? ? ? ?
2 4 5 , and 2 3 i j k i j k ? + - + +
? ?
is equal the one. Find the value of ?
[4]
10. Find the area of the ? with vertices A (1, 1, 2) B (2, 3, 5) and C (1, 5, 5).
[4]
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