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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

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

4.
Find 2, 3  . 4 a b if a b and a b - = = =
     

5.
If
? ? ?
4 3 2 3 2 2 a i j k b i k find b a = + + = + ×
   
? ?

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.

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.

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 + - = + + = + +
     
? ?

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 ?

10. Find the area of the ? with vertices A (1, 1, 2) B (2, 3, 5) and C (1, 5, 5).

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