Question

Write 25 important.point used in vectors

Answer 1

Answer:

A study of motion will involve the introduction of a variety of quantities that are used to describe the physical world. Examples of such quantities include distance, displacement, speed, velocity, acceleration, force, mass, momentum, energy, work, power, etc. All these quantities can by divided into two categories - vectors and scalars. A vector quantity is a quantity that is fully described by both magnitude and direction. On the other hand, a scalar quantity is a quantity that is fully described by its magnitude. The emphasis of this unit is to understand some fundamentals about vectors and to apply the fundamentals in order to understand motion and forces that occur in two dimensions

Answer 2

lmportant points used in vectors ---------~~~~~~~~~

$1. |p| - |q| \leqslant |p + q \leqslant |p| + |q|$

$2. \: \: if \: |p +q | = p + q \\ then \: \theta \: = 0 \degree \: \\ 3.if \: | p+q | = p - q \\ then \: \: \theta \: = 180 \degree \: \\ 4.if \: | p+q | = \sqrt{ |p| + |q| } \\ then \: \theta \: = 90 \degree \\ 5.if \: |p| = |q| \: \: \: \\ then \: r \: = 2p \: cos \ \frac{ \theta}{2} \\ 6. \: if \: |p| + |q| \: and \: \theta \: = 120 \degree \: \: \\ then \: r = p$

7. minimum number of factors required to give 0 resultant is 2.

8. minimum number of non collinear vectors required to give 0 resultant is 3.

the three vectors should be coplanar and must form a closed triangle when taken in order.

9. dot product of perpendicular vectors is zero.

10. cross product of parallel vectors is zero.

11.î×î = 0

12. J cap into J cap i = 0

13. K cap × k cap = 0

14. area of parallelogram is equals to AB sin θ

15. director can have maximum number of 3 rectangular component.

16. the resultant of P and Q is P then magnitude of difference is root 3 p.

17. î.î=1

18. j.j =1

19. k.k=1

20. î.j =0

21 j.k= 0

22. k.î = 0

$23. \: \: cos ^{2} \alpha + {cos}^{2} \beta + {cos}^{2} \gamma = 1$

24. cross product of two vectors is perpendicular to both of them.

25.$a.b \: = ab \cos( \theta)$