Ch 7 Maths Class 12 Solutions

Complete Handwritten notes of Ch 7 Maths Class 12 Solutions written by Mr. M Sulman Sherazi Suib. These notes are very helpful in the preparation of Ch 7 Maths Class 12 Solutions pdf for the students of the intermediate and these are according to the paper patterns of all Punjab boards.

Summary and Contents:
Topics which are discussed in the notes are given below:
  • Important ch 7 maths class 12 important questions for Intermediate part-II students.
  • Scalar: A quantity which has magnitude only is called scalar, e.g., time, volume, speed and work etc. The Scalars are denoted by letters.
  • Vector: A quantity which has both magnitude and direction is called vector. 2.9., Velocity, city, displacement, force and torque etc. A vector (say v) is denoted by or or by bold face letter v.
  • Important ch 7 maths class 12 for Intermediate part-II students.
  • Geometrical interpretation of vector:  Geometrically, a vector is represented by a line segment AB with A its initial point and Bits terminal point. It is often found convenient to denote a vector by an arrow and is written either as AB or as a boldface symbol like or in underlined formy.
  • Important class 12 maths 7.1 for Intermediate part-II students.
  • Magnitude of a vector:- Let vbe a vector, then its magnitude is denoted by IvI or simply v. It is also called norm or length of vector. If the line AB represents a vector, then distance from pt. A to pt. B will be magnitude of AB and is denoted by IABI.
  • Unit vector: A vector whose magnitude is one (unity) is called unit vector. Unit vector of vis written as (read as vhat) and is defined as; 
  • Important class 12 maths ch 7 for Intermediate part-II students.
  • Null vector:- A vector whose magnitude is zero but no specific direction is called noll or zero vector. It is denoted by 0.
  • Negative vectors:- Two vectors are said to be negative of each other if they have same magnitude but opposite direction. If ABV then BA-AB=-V and IBN-1-ABI ("The magnitude of a vector is a non-negative nomber).
  • Important class 12 maths ch 7 ex 7.1 for Intermediate part-II students.
  • Multiplication of vector by a Scalar: Let k be a scalar number (K belong to R) and be a vector, then KV is a vector which is k times. to vector. (ⅰ) and Ky are in same direction if K>0. (ii) and KỸ are in opposit direction if k
  • Important class 12 maths ch 7 ex 7.2 for Intermediate part-II students.
  • Equal vectors: Two vectors AB and có are said to be equal, if they have the same magnitude and same direction.i-e., | ABI-KI
  • What are scalars and vectors in mathematics?
  • Important class 12 maths ch 7 ex 7.3 for Intermediate part-II students.
  • Geometric interpretation of factors
  • Formulas of Magnitude or length or norm of a vector
  • Multiplication of vector by a scalar
  • Important ex 7.1 class 12 maths solutions for Intermediate part-II students.
  • Addition and subtraction of two vectors
  • Triangle Law of addition and parallelogram of the law of addition subtraction of two vectors position vectors
  • Vectors in a plane scalar, multiplication of a vector, negative of a vector, difference of two vectors, zero vectors, equal vectors, position vectors, magnitude of vectors. 
  • Important ex 7.2 class 12 maths solutions for Intermediate part-II students.
  • Properties of the magnitude of a vector, another notation for representing vector in the plane.
  • A unit to vector in the direction of another given vector
  • Vector geometry 
  • Important exercise 7.3 class 12 maths solutions for Intermediate part-II students.
  • Introduction of vector in space Introduction of vector in space and Properties of vectors.
  • Another notation for representing the vectors in space.
  • Distance between two points in space with examples
  • Direction angles and direction cosines of a vector.
  • The scalar product of two vectors
  • Deductions of important results
  • Perpendicular orthogonal vectors or properties of a dot product
  • Analytical expression of door product (Dot product of factors in the form of their components)
  • The angle between two vectors Formula
  • Projection of one vector upon another vector.
  • The cross product or the vector product of two vectors.
  • Properties of cross product.
  • Area of parallelogram area of the triangle with their examples.
  • The volume of a parallelepiped formula
  • The formula of the volume of the Tetrahedron.
  • Application of vectors in physics and Engineering.
  • Derivation of useful results of cross-products
  • Find the cosine of the angle between
  • Find a unit vector perpendicular to u and v
  • Direction angles of vector
  • Find the magnitude of
  • Vector product of two vectors
  • Definition of a unit vector
  • Direction angles and direction cosines
  • Important class 12 maths exercise 7.1 for Intermediate part-II students.
  • Important class 12 maths exercise 7.2 for Intermediate part-II students.
  • Important class 12 maths exercise 7.3 for Intermediate part-II students.
  • Important class 12 maths exercise 7.4 for Intermediate part-II students.

Loading your document...

Download PDF