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VECTOR IN PLANE

VECTOR. VECTOR IN PLANE. THE PURPOSE OF LEARNING :. VECTOR. The students have ability to develop their skill in doing, applying, and solving daily life problem that connected with vector. CS :. Applying vector concept in solving a problem. BC :. Applying vector in a plane

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VECTOR IN PLANE

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  1. VECTOR VECTOR IN PLANE

  2. THE PURPOSE OF LEARNING: VECTOR The students have ability to develop their skill in doing, applying, and solving daily life problem that connected with vector. CS: Applying vector concept in solving a problem BC : Applying vector in a plane Applying vector concept in polyhedral Isi dengan Judul Halaman Terkait

  3. VECTOR MAATREGEL VECTOR SCALAR Have direction (force, speed, Distance, etc) Doesn’t have direction (length, mass, time, temperature, etc) Isi dengan Judul Halaman Terkait

  4. 600 P2 = 4 KN P1 = 5 KN Learning Experience VECTOR • 1. How big id the force resultant in a pulley that is shown in the following picture. Isi dengan Judul Halaman Terkait

  5. 1 To left – 4 – 4 – 4 – 4 • KE KIRI • KE KIRI • KE KIRI 2 2 2 2 2 KE ATAS 2 KE ATAS 2 To upward 2 KE ATAS VECTOR IN A PLANE LOOK AT THE DIRECTED LINE SEGMENT BELOW EVERY DIRECTED LINE SEGMENT REPRESENT THE SAME SHIFTING: • TO LEFT 2 TO UPWARD SYMBOL – 4 EVERY DIRECTED LINE SEGMENT ABOVE REPRESENT A VECTOR 2 Isi dengan Judul Halaman Terkait

  6. – 5 – 5 – 5 5 TO LEFT 5 KE KIRI 5 KE KIRI –4 – 4 –4 4 KE BAWAH 4 KE BAWAH 4 To downward – 5 – 4 VECTOR IN A PLANE 5 TO LEFT 4 DOWNWARD EVERY DIRECTED LINE SEGMENT REPRESENT THE SAME SHIFTING: SYMBOL EVERY DIRECTED LINE SEGMENT ABOVE REPRESENT A VECTOR Isi dengan Judul Halaman Terkait

  7. Q B P A Exercise VECTOR • Draw a line segment through point A that parallel with and a perpendicular line segment through point B. Isi dengan Judul Halaman Terkait

  8. Q E 3 C B 1 3 D P 3 3 1 A 1 1 Solution: VECTOR IN A PLANE Isi dengan Judul Halaman Terkait

  9. POSITION VECTOR If point P is a point in Cartesian plane, then vector = P (x1,y1) If the coordinate of pointP(x1,y1) then position vector from point P is: p y1 Is called vector component of p X1 is a vector that have length one unit. Unit vector Unit vector with direction of X axis is called Unit vector with direction of X axis is called Isi dengan Judul Halaman Terkait

  10. p = x1 i + y1 j x1 and y1 is called the components vector p VECTOR IN PLANE VECTOR IN THE FORM OF LINEAR COMBINATION Look at the vector p below: P (x1,y1) X If point P(x1,y1) then OP = OQ + QP It can be stated in basis vector: Isi dengan Judul Halaman Terkait

  11. VECTOR IN A PLANE VECTOR LENGTH The vector length is can be drawn by directed line. It is the length of directed line segment. p P(x1,y1) o Q Then, the vector length So, if is Isi dengan Judul Halaman Terkait

  12. VECTOR IN A PLANE Exercise sample • Stated the position vector of point A (5,3)as basis vector (linier combination of i and j) Answer : vector a or = 5i + 3j • Stated the position vector of point A (3,2,- 4)as basis vector (linier combination of i, j and k) Answer: vektor a or = 3i + 2j – 4 k • Stated vector as basis vector (linear combination of i and j) if point A (5,-3)and B (3,2) Answer : Isi dengan Judul Halaman Terkait

  13. VECTOR IN A PLANE Vector Addition If vector a is added with vector b, we will get vector c. it is denoted by How • Triangle way • Parallelogram way Isi dengan Judul Halaman Terkait

  14. b a AC = AB + BC c = a + b VECTOR IN A PLANE Triangle Way Move vector b so the initial is joint with the end of vector a C a + b = c B A B Isi dengan Judul Halaman Terkait

  15. Move vector b, so the initial is join with the initial of vector a a b b a VECTOR IN A PLANE Parallelogram way a + b = c Isi dengan Judul Halaman Terkait

  16. Define vector AE into vector u and v ? How about vector EF ? VECTOR IN APLANE EXERCISE SAMPLE Isi dengan Judul Halaman Terkait

  17. E D C F A B VECTOR IN A PLANE Isi dengan Judul Halaman Terkait

  18. b b a a VECTOR IN A PLANE Vector Subtraction The rest of vector a and vector b is vector c that get from adding vector a with vector b a - b = a + ( -b) a – b = a + (-b) = (-b) +a = PS + ST = PT = RQ R P Q -b S a T Isi dengan Judul Halaman Terkait

  19. Vector in a Plane The multiplication result of real number k with vector a is vector that the length |k| is multiplied by the length of vector a and the direction is: • Equal to the direction of vector a if k > 0 opposite the direction of vector a if k < 0 • Equal to zero if k = 0 Isi dengan Judul Halaman Terkait

  20. Vector in a Plane If vector In the form of line segment Isi dengan Judul Halaman Terkait

  21. Vector in a Plane If vector In the form of line segment Isi dengan Judul Halaman Terkait

  22. Vector in a Plane Show in vector picture Isi dengan Judul Halaman Terkait

  23. VECTOR . . . ? In algebra, vector in two dimensional (R2) is orderly pairs of real numbers [x, y], x and y is the components of those vectors and in three dimensional (R3) vector is orderly pairs of real number [x, y, z] x, y and z is the components of those vectors. In geometric, vector is a set of directed line segment. The length of directed line segment shows the size,while the arrow direction shows the vector direction Isi dengan Judul Halaman Terkait

  24. POSITION VECTOR If point P is a point in Cartesian plane, then vector = P (x1,y1) If the coordinate of pointP(x1,y1) then position vector from point P is: p y1 Is called vector component of p X1 is a vector that have length one unit. Unit vector Unit vector with direction of X axis is called Unit vector with direction of X axis is called Isi dengan Judul Halaman Terkait

  25. VECTOR IN POLYHEDRAL Unit vector with the direction of Y axis is called Unit vector that have the same direction with Z axis is called Isi dengan Judul Halaman Terkait

  26. VECTOR IN POLYHEDRAL VECTOR LENGTH So, if Then, the vector length is Known two points A (x1, y1,z1) and B (x2, y2, z2) In polyhedral, the length of AB is formulated as follows : Isi dengan Judul Halaman Terkait

  27. B n P b p m A O a Vctor in a Plane Division formula In the form of coordinate If point P is in line segment AB then it can be stated: • In the form of vector Isi dengan Judul Halaman Terkait

  28. VECTOR IN POLYHEDRAL Scalar multiplication from two vectors If and The multiplication result of two vectors and is Isi dengan Judul Halaman Terkait

  29. VECTOR IN POLYHEDRAL The multiplication result of two vectors a and b. If both of them make certain angle. It is defined: a.b = Cos  where :the angle between vector a and b The angle between vector a and b can be determined by: Isi dengan Judul Halaman Terkait

  30. axb b  a bxa VECTOR IN POLYHEDRAL The cross product of two vectors The cross product of vector and is defined: If vector and Vector Then the cross product of two vectors are formulated as follows: Perkalian silang dua matriks bisa juga diselesaikan menggunakan Determinan 3x3 dengan cara Sarrus Isi dengan Judul Halaman Terkait

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