2nd Year Math Chapter 7 Notes
Important handwritten short notes of 2nd Year Math Chapter 7 Notes written by Professor Asad Khalid Suib. These notes are very helpful in the preparation of 2nd year math chapter 7 notes pdf download 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 2nd year math chapter 7 mcqs for Intermediate part-II students.
- 1. Cross product or vector product is defined
- (a) In plane only (b) in space only (c) everywhere (d) in vector field
- 2. If u and v are two vectors , then u×v is a vector
- (a) Parallel to u and v (b) parallel to u (c) perpendicular to u and v (d) orthogonal to u
- 3. If u and v be any two vectors, along the adjacent sides of ||gram then the area of ||gram is
- (a) u×v (b) |u×v| (c) 1/2(u×v) (d) 1/2|u×v |
- 4. If u and v be any two vectors, along the adjacent sides of triangle then the area of triangle is
- (a) u×v (b) |u×v| (c) 1/2(u×v) (d) 1/2|u×v |
- Important 2nd year math ch 7 mcqs for Intermediate part-II students.
- 5. Two non zero vectors are perpendicular iff
- (a) u.v=1 (b) u.v≠1 (c) u.v≠0 (d) u.v=0
- 6. The scalar triple product of a ,b and c is denoted by
- (a) a.b.c (b) a.b×c (c) a×b×c (d) (a+b)×c
- Important 2nd year maths chapter 7 mcqs for Intermediate part-II students.
- 7. The vector triple product of a ,b and c is denoted by
- (a) a.b.c (b) a.b×c (c) a×b×c (d) (a+b)×c
- 8. Notation for scalar triple product of a ,b and c is
- (a) a.b×c (b) a×b.c (c) [ a.b.c]) (d) all of these
- 9. If the scalar product of three vectors is zero, then vectors are
- (a) Collinear (b) coplanar (c) non coplanar (d) non-collinear
- Important 2nd year maths chapter 7 mcqs solved for Intermediate part-II students.
- 10. If any two vectors of scalar triple product are equal, then its value is equal to
- (a) 1 (b) 0 (c) -1 (d) 2
- Important 2nd year maths chapter 7 mcqs with answers for Intermediate part-II students.
- 11. Moment of a force F about a point is given by:
- (a) Dot product (b) cross product (c) both (a) and (b) (d) None of these
- Important 2nd year math chapter 7 important questions for Intermediate part-II students.
- Parallel vectors: - Two vectors & and are said to be parallel if u = KV or J=ku. If u = kỳ then i and vare in same direction if Ko, Also and Jare in opposite direction if K<0. of Addition of two vectors
- Important 2nd year math exercise 7.1 solution pdf for Intermediate part-II students.
- Addition of two vectors is explained by following two laws:
- (i) Triangle Law of addition: If two vectors a and b are represented by two sides AB and BC of AABC s.that the terminal point of a coincide with the initial point of b. then the third side Ac of the triangle gives vector sum a+b: i-e, AB+ BC = AC a+b = AC
- (ii) Parallelogram Law of Addition: If two vectors u and ✓ are represented by two sides AB and AC of Ilgram as shown in fig, then diagonal AD give the sum of AB and AC (-e., AB = AB+ AC = u+v
- Important 2nd year math chapter 7 for Intermediate part-II students.
- Position Vector: The vector whose initial point is at origin O and terminal point is at P is called position vector of point P.
- Corollary: If P is the midpoint of AB, then p:q = 1:1
- Note: The dot product is also referred to the scalar product or the inner product.
- Application of vectors in Physics and Engineering: (a) Work done: If d is displacement (from A to B) when force F is applied on the particle then work done = (force).(Displacement)
- 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 2nd year maths chapter 7 exercise 7.1 for Intermediate part-II students.
- Important 2nd year maths chapter 7 exercise 7.2 for Intermediate part-II students.
- Important 2nd year maths chapter 7 exercise 7.3 for Intermediate part-II students.
- Important 2nd year maths chapter 7 exercise 7.4 for Intermediate part-II students.