CHAPTER 1 VECTOR SCALARS AND and has magnitude     r r x y z 2 2 2 Definition: A unit vector is a vector having unit magnitude. If is a vector with A magnitude 0 then, is a unit vector having the same A A A  aˆ direction as . A Example 1.3 Find the unit vector paralleled to the resultant of vectors:  2iˆ  4 5kˆ ,   2  3kˆ r1 r2 iˆ ˆj ˆj Resultant    6 2k     R r1 r 3ˆ ˆ 2 32 62   3iˆ  6 2kˆ  R R   ˆj 2 7  6 2kˆ. Then a unit vector parallel to is    R rˆ R R ˆj 1 Verify that rˆ 7 has magnitude 1. Example 1.4 Determine the vector having initial point P (x1, x1, x1) and terminal point Q (x2, y2,z2) and find its magnitude. Z P(X,Y,Z Q(X,Y,Z Y r1 r 2 O X The position vector of P is    r1 x1iˆ y1 z1kˆ ˆj The position vector of Q is r  x2iˆ  y2  z2kˆ ˆj 2
CHAPTER 1 VECTOR AND SCALARS and has magnitude r  r  x 2  y 2  z 2 Definition: A unit vector is a vector having unit magnitude. If A is a vector with magnitude A 0 then, A A  aˆ is a unit vector having the same direction as A . Example 1.3 Find the unit vector paralleled to the resultant of vectors: r1  2iˆ  4 ˆj 5kˆ , r2  iˆ  2 ˆj  3kˆ Resultant R  r1  r 2     3ˆ  6 ˆ 2k R  R  3iˆ  6 ˆj 2kˆ  32  62   7 Then a unit vector parallel to R is rˆ  R R  1 7  6 ˆj 2kˆ. Verify that rˆ has magnitude 1. Example 1.4 Determine the vector having initial point P (x1, x1, x1) and terminal point Q (x2, y2,z2) and find its magnitude. Z P(X,Y,Z X r1 O r 2 Q(X,Y,Z Y The position vector of P is r1  x1iˆ  y1 ˆj  z1kˆ The position vector of Q is r 2  x2iˆ  y2 ˆj  z2kˆ 2