CBSE Class 12 Maths Notes Chapter 11 Three Dimensional Geometry Direction Cosines of a Line: If the directed line OP makes angles α, β, and γ with positive X-axis, Y-axis and Z-axis respectively, then cos α, cos β, and cos γ, are called direction cosines of a line. They are denoted by l, m, and n. Therefore, l = cos α, m = cos β and n = cos γ. Also, sum of squares of direction … [Read more...]
Vector Algebra Class 12 Notes Maths Chapter 10
CBSE Class 12 Maths Notes Chapter 10 Vector Algebra Vector: Those quantities which have magnitude, as well as direction, are called vector quantities or vectors. Note: Those quantities which have only magnitude and no direction, are called scalar quantities.Representation of Vector: A directed line segment has magnitude as well as direction, so it is called vector denoted … [Read more...]
Probability Class 12 Notes Maths Chapter 13
CBSE Class 12 Maths Notes Chapter 13 Probability Event: A subset of the sample space associated with a random experiment is called an event or a case. e.g. In tossing a coin, getting either head or tail is an event.Equally Likely Events: The given events are said to be equally likely if none of them is expected to occur in preference to the other. e.g. In throwing an … [Read more...]
Linear Programming Class 12 Notes Maths Chapter 12
CBSE Class 12 Maths Notes Chapter 12 Linear Programming Linear Programming Problem: A linear programming problem is one in which we have to find optimal value (maximum or minimum) of a linear function of several variables (called objective function) subject to certain conditions that the variables are non-negative and satisfying by a set of linear inequalities with variables, … [Read more...]
Differential Equations Class 12 Notes Maths Chapter 9
CBSE Class 12 Maths Notes Chapter 9 Differential Equations Differential Equation: An equation involving independent variable, dependent variable, derivatives of dependent variable with respect to independent variable and constant is called a differential equation. e.g.Ordinary Differential Equation: An equation involving derivatives of the dependent variable with … [Read more...]