Page 1 CBSE TEST PAPER04 CLASS  XII MATHEMATICS (Vectors & Three Dimensional Geometry) Topic:  Vectors [ANSWERS] Ans1. Scalar Ans2. ( ) ( ) ( ) 2 2 2 2 7 3 b = +  +  4 49 9 62 = + + = Ans3. D.R of 1,2, 1 r are  1 4 1 6 r = + + = D.C of 1 2 1 , , 6 6 6 r are  Ans4. 1 a = ( ) ( ) 2 . 8 1 8 x a x a x  + =  = 2 2 9 3 x x = = Ans5. ( ) ( ) . . L H S a b a b =  × + 0 0 a a a b b a b b a b a b = × + ×  ×  × = + × + ×  ( ) 0 2 a b a b a b b a ? × = = × ? × =  × ? ? ? Ans6. 0 a b c + + = ( ) . 0 . . . 0 a a b c a a a b a c + + = + + = Page 2 CBSE TEST PAPER04 CLASS  XII MATHEMATICS (Vectors & Three Dimensional Geometry) Topic:  Vectors [ANSWERS] Ans1. Scalar Ans2. ( ) ( ) ( ) 2 2 2 2 7 3 b = +  +  4 49 9 62 = + + = Ans3. D.R of 1,2, 1 r are  1 4 1 6 r = + + = D.C of 1 2 1 , , 6 6 6 r are  Ans4. 1 a = ( ) ( ) 2 . 8 1 8 x a x a x  + =  = 2 2 9 3 x x = = Ans5. ( ) ( ) . . L H S a b a b =  × + 0 0 a a a b b a b b a b a b = × + ×  ×  × = + × + ×  ( ) 0 2 a b a b a b b a ? × = = × ? × =  × ? ? ? Ans6. 0 a b c + + = ( ) . 0 . . . 0 a a b c a a a b a c + + = + + = 2 . . . . 1 ( ) a b a c a a b a c i + =  + =         . . 16 ( ) . . 4 ( ) b a b c ii a c b c iii + =       + =       Adding (i) (ii) and (iii) ( ) 2 . . . 21 21 2 a b b c a c µ + + =   = Ans7. 1 1  Let to ß ?a ß a ? = ? ? ? ( ) ? 1 3 3 i j i j ß ? ? ? =  =  ? ? ? ? ( ) ? ( ) 2 1 2 3 3 i j k i j ß ß ß ? ? =  = +    ? ? ( ) ( ) ? ? 2 2 2 3 1 3 . 0 i j k ? ? a ß ß a =  + +  ? = ? ? ? ? ( ) ( ) 3 2 3 1 0 1 2 ? ? ?   + = = ? ? ? 1 2 3 1 2 2 1 3 3 2 2 i j i j k ß ß =  = +  ? ? Ans8. 0 a b c + + = a b c + =  ( ) ( ) ( ) ( ) ( ) . . . . a b c c c a b a b c c +  =   + + = 2 2 2 2 49 9 25 15 . 2 2 a ab b c a b + + =   = = Page 3 CBSE TEST PAPER04 CLASS  XII MATHEMATICS (Vectors & Three Dimensional Geometry) Topic:  Vectors [ANSWERS] Ans1. Scalar Ans2. ( ) ( ) ( ) 2 2 2 2 7 3 b = +  +  4 49 9 62 = + + = Ans3. D.R of 1,2, 1 r are  1 4 1 6 r = + + = D.C of 1 2 1 , , 6 6 6 r are  Ans4. 1 a = ( ) ( ) 2 . 8 1 8 x a x a x  + =  = 2 2 9 3 x x = = Ans5. ( ) ( ) . . L H S a b a b =  × + 0 0 a a a b b a b b a b a b = × + ×  ×  × = + × + ×  ( ) 0 2 a b a b a b b a ? × = = × ? × =  × ? ? ? Ans6. 0 a b c + + = ( ) . 0 . . . 0 a a b c a a a b a c + + = + + = 2 . . . . 1 ( ) a b a c a a b a c i + =  + =         . . 16 ( ) . . 4 ( ) b a b c ii a c b c iii + =       + =       Adding (i) (ii) and (iii) ( ) 2 . . . 21 21 2 a b b c a c µ + + =   = Ans7. 1 1  Let to ß ?a ß a ? = ? ? ? ( ) ? 1 3 3 i j i j ß ? ? ? =  =  ? ? ? ? ( ) ? ( ) 2 1 2 3 3 i j k i j ß ß ß ? ? =  = +    ? ? ( ) ( ) ? ? 2 2 2 3 1 3 . 0 i j k ? ? a ß ß a =  + +  ? = ? ? ? ? ( ) ( ) 3 2 3 1 0 1 2 ? ? ?   + = = ? ? ? 1 2 3 1 2 2 1 3 3 2 2 i j i j k ß ß =  = +  ? ? Ans8. 0 a b c + + = a b c + =  ( ) ( ) ( ) ( ) ( ) . . . . a b c c c a b a b c c +  =   + + = 2 2 2 2 49 9 25 15 . 2 2 a ab b c a b + + =   = = . cos 1 2 60 a b a b ? ? = = = Ans9. ? ? 3 1 2 1 3 4 i j k a b × =   ? ? ? ( ) ( ) ( ) 2 2 2 2 14 10 . 2 14 10 10 3 i j k req area a b =    = × =  +  +  = ? Ans10. ( ) ( ) ? ( ) ? 1 2 2 3 4 0 PQ i j k =   +   +   ? ? ? 3 5 4 3, 5, 4 i j k DR are =       ? 9 25 16 3 5 4 . , , 50 50 50 PQ D C are = + +   Read More
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