VECTOR VECTOR IN PLANE

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

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

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

EVERY DIRECTED LINE SEGMENT REPRESENT THE SAME SHIFTING: 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 2 KE ATAS 2 KE KIRI – 4 2 KE ATAS 2 KE KIRI – 4 KE KIRI – 4 2 KE ATAS 2 1 To left 2 To upward 2 – 4 – 4 EVERY DIRECTED LINE SEGMENT ABOVE REPRESENT A VECTOR 2 Hal.: 5 Isi dengan Judul Halaman Terkait

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

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

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

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

It can be stated in basis vector: Isi dengan Judul Halaman Terkait 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: p = x1 i + y1 j x1 and y1 is called the components vector p Hal.: 10 Isi dengan Judul Halaman Terkait

Isi dengan Judul Halaman Terkait 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 Hal.: 11 Isi dengan Judul Halaman Terkait

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

Isi dengan Judul Halaman Terkait 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 Hal.: 13 Isi dengan Judul Halaman Terkait

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

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

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

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

Isi dengan Judul Halaman Terkait 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 b b P Q a -b a S a T Hal.: 18 Isi dengan Judul Halaman Terkait

Isi dengan Judul Halaman Terkait 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 Hal.: 19 Isi dengan Judul Halaman Terkait

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

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

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

Isi dengan Judul Halaman Terkait 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 Hal.: 23 Isi dengan Judul Halaman Terkait

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

Isi dengan Judul Halaman Terkait 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 Hal.: 25 Isi dengan Judul Halaman Terkait

Isi dengan Judul Halaman Terkait 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 : Hal.: 26 Isi dengan Judul Halaman Terkait

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

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

Isi dengan Judul Halaman Terkait 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: Hal.: 29 Isi dengan Judul Halaman Terkait

Isi dengan Judul Halaman Terkait VECTOR IN POLYHEDRAL b  axb a bxa 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 Hal.: 30 Isi dengan Judul Halaman Terkait