Page 170 - Advanced engineering mathematics

150 CHAPTER 6 Vectors and Vector Spaces

z
z
F + G F + G G
G

F
F

y
y

x
x
FIGURE 6.4 Parallelogram law for vector
addition. FIGURE 6.5 Alternative view of the
parallelogram law.
z

(0,0,1)
k
y
j (0,1,0)
i
(1,0,0)
x

FIGURE 6.6 Unit vectors i, j, and k.

lengths of any two sides of a triangle must be at least as great as the length of the third side, we
have the triangle inequality

F + G ≤ F + G .

A vector of length 1 is called a unit vector. The unit vectors along the positive axes are
shown in Figure 6.6 and are labeled

i =< 1,0,0 >, j =< 0,1,0 >, k =< 0,0,1 >.

We can write any vector F =< a,b,c > as
F =< a,b,c > = a < 1,0,0 > +b < 0,1,0 > +c < 0,0,1 >
= ai + bj + ck.

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October 14, 2010 14:21 THM/NEIL Page-150 27410_06_ch06_p145-186