Page 1 CBSE TEST PAPER-04 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 PAPER-04 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 PAPER-04 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