SAMPLE PAPER

-12  ( ˜)

 

 3 U                                                                                                          Z  35

 

(I) U

          (II) U

 

1. ِ U U U U                           ( 1 )

() y j+2j-k 

() (2,3,4) 3i+4j+5k  U U U 跤U

() U 3 UU/𷤇U U 8 UU/𷤇U U U U U U U

() 5 U ߢ 4 U U P Q U ܻ U PQ=10 UU, QR ܐ , U R U U

(U.) U U U U, U U t 𷤇U (T2-4) /𷤇U 2 U # U U U Uⷤ U U

 

2.  ِ U U U U                         ( 1 )

() 10 ‡U 20 US U U Uⷤ

() a=2i-3j+4k b=2i+7k 7a-4b 

() 56 44 UU UU U բ U, U U UU U UU

() (A+B) (A-B) U U, U (A2+B2)1/2  U

(U.) 100 U U 10 U U S U

 

3. ِ U U U U                           ( 1 )

() 218 U U U U UU U 54.5 ̷ U [I=981 /2]

() a=2j-3k    b=3i+2j-k axb U

() 2,4,8 U 16 緤 U U UU U U U U U U L 𴤼 U ٷ

() U ܻ U , U U 𤷤

(U.) I UU 𴤷 U 2 𷤇U S

 

4. ِ U U U                                   ( 2 )

() h ׿ ߷ USU ׷ U U U

() 2m, 4m U 6m S U U U U  24 U UU U, U ȤU U U UU U ⢃^U U

() 30 緤 150 U U 500 / U U U U ܻ U UU U UU U L

() h ABC A,B C S 2i-j+k, i-3j-5k U 3i-4j-k U, ׷ U

(U.) 2 緤 U ‡U 4/ ܷU 4 緤 U ‡U U US U, ⢃UUU U U ⢃UUU 𤷤U NU

 

5. ِ U U                                   ( 2 )

() SU (4,1,-3) (3,1,-1) mU U U (1,2,3) (5,4,1) ̷ S U U mU ٷ

() -2i+3j+k UU U i+j+k L i+2j+3k U U

() ‡U U U U U U F U ȤU ע f U U U t 𷤇U U 50 U h U  t(FF)1/2=10(F+F)1/2

() U 50 UU/𷤇U U U U U U U U U UU

 

6. ِ U U                            3

() h (axb).(cxd) = (a.c) (b.d) -  (a.d) (b.c) 

() ǸU U U , U w r  U U 𴤼 U F ܻ淤U h LU U U U h UF    w (2rh-h2)1/2 /r-h    U U

 

7. ِ U U                           3

() (i+2j-k)  r(3i-j+k) =1    r(i+4j-2k)=2 ̑U U U ܐ 跤U U

() U U ǸU X U U 45 U 𴤷 U U U U U U U U U U y U U U U h U XY/X+Y U

 

8. ِ U U                           3

() 28  UU ܐ U U U UU U 45 U U U ɸ U U ɸU U 1/3 U 1/2 U U ɸU U U, ɸU U ɸU ɸU Ȥ ̷ U U U

() v U 8 緤/U UU U U U U U UU } UU U U U U, U } -U U U U U U

 

 

U

1.   S U

2. U UU U U U CU U

3. ܃ } U v SU U

4. U ̉ UU U

5. U U U U ǸUUU U

  U       ן         v

 

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