Algebra Formulas For Class 12

1 VECTOR ALGEBRA & 3D Weightage 17 Marks SYLLABUS: 1. VECTOR ALGEBRA Vectors and scalars, magnitude and direction of a vec...2 1. If a unit vector a  makes angles 3  with i , 4  with j and an acute angle  with k  , find the value of  . 1 2...3 Condition for two vectors to be parallel ba  . OR 2 1 2 1 2 1 c c b b a a  7)   bababa  .2 2 22  ;  ...4 ONE MARKER 1. For the following points A, B find the vector AB  as well as their magnitudes A (2, -1, 3), B (0, -5, ...5 23. Find projection & projection vector of a  on b  for 5 3 4 , 6 8a i j k b i j k            24. For 3 ...6 THREE – DIMENSION GEOMETRY SYLLABUS Direction cosines and direction ratios of a line joining two points. Cartesian and v...7 3. The points A(4, 5, 10), B(2, 3, 4) and C(1, 2, –1) are three vertices of a parallelogram ABCD. Find the vector equati...8 S. D. =  2 1 1 2 1 2 ( ).( )a a m m m m          OR S.D. =   2 1 2 1 2 1 1 1 1 2 2 2 2 1 2 2 1 x x y y z z ...9 8. Equation of plane that contains the lines 1 1 1 1 1 1 c zz b yy a xx      & 2 1 2 1 2 1 c zz b yy a xx     ...10 2. Equation of line perpendicular to plane a x + by + c z + d = 0 and passing through the point ( x1, y1, z1) is c zz b...11 19. Find the plane passing through the point (2, 1, 4) and parallel to the lines 4 6 3 1 2 1      zyx and 4 7 1 6 ...12 LINEAR PROGRAMMING Weightage 6 Marks SYLLABUS Introduction, related terminology such as constraints, objective function...13 which collects drainage from this land. How much land should be allocated to each crop so as to maximise the total prof...14 PROBABILITY Weightage 10 Marks Conditional probability, multiplication theorem on probability. independent events, tota...15 2013 1. A speaks truth in 60% of cases, while B in 90% of the cases. In what percentage of cases are they likely to con...