math 2: vectors Flashcards
a vector in a plane is defined to be an
ordered pair of real numbers
a vector in space is defined as an ordered
triple of real numbers
a vector is usually represented by an arrow whose initial point is the o
origin and whose terminal point is at the ordered pair or triple that named the vector
vector quantities always have a magnitude or norm (…) and direction (…)
the length of the arrow; the angle the arrow makes with the axes
if vector →V is designated by (v1, v2) and vector →U is designated by (u1, u2) vector →U+V is designated by
(u1 + v1, u2 + v2), called the resultant of U and V
Vector - →V has the same .. as →V but has a … opposite that of →V
magnitude; direction
on the plane, every vector →V can be expressed in terms of any other two unit (magnitude 1) vectors parallel to the
x- and y- axes
if vector → i = (1, 0) and vector → j = (0, 1), any vector →V =
ai + bj, where a and b are real numbers
a unit vector parallel to →V can be determined by dividing →V by its norm, denoted by
||→V|| and equal to root (asquared + bsquared)
dot product/inner product of two vectors →V (v1, v2) and →U (u1, u2) is
→V . →U = v1u1 + v2u2
dot product of two vectors is a
real number, not a vector
two vectors, v and u, are perpendicular if and only if
V . U = 0
