In an `Delta ABC` as showin in Fig. 2 . (2) .71 (a) prove
that ` a/(sin A) =b/(sin B) =C/(sin C)`.

Explanation

Refer to fig .2 (c ) . 71 (b). Mbrgt vectors ` vec a, vec b and vec c` are repesented by the three sides of a triangle taken in one order. Their resultant is zero. So
.
` vec a + vec b + vec c=0` ltvegt or ` vec a + vec b =- vec c`
or `(vec a + vec b) xxx vec c =- vec c xx vec c =0`
or ` vec a xx vec c + vec b cc vec c =0 or -vec c xx vec a + vec b+ vec c=0`
or ` vec b xx vec c =vec c xx vec a` ..(i)
Similarly we can get
` vec axx vec b = vec b xx vec c` (ii)
Form (i) and (ii),
` vec a xx vec b = vec b xx vec c = vec c xx vec a`
or ` | vec a xx vec b | = vec b xx vec c|= | vec c xx vec a|`
or ` ab sin (180^(@) -C) = bc sin (80^(@) -A)`
`=ca sin (180^(@) -B)
or an sin C= sin A = ca sin B`
Dividing it by abc we get
` (sin C)/c =(Sin A)/a =(sin B)/b`
or ` a/(sin A)= b /(sin B) = c/(sin C)` (Proved)`