vectors! scalars! HELP!!?

3 ⤊

vectors! scalars! HELP!!?

write c in the form ra+sb, where r and s are scalars.

a=3i+2j
b+8i+5j
c+7i+9j

2007-10-03 18:56:18 · 2 answers · asked by Jebediah T 1 in Science & Mathematics ➔ Mathematics

2 answers

Assume question SHOULD read as:-
a = 3i + 2j
b = 8i + 5j
c = 7i + 9j

ra = 3r i + 2r j
sb = 8s i + 5s j

ra + sb = (3r + 8s) i + (2r + 5s) j
c = 7 i + 9 j
If c = ra + sb:-
3r + 8s = 7
2r + 5s = 9

-6r - 16s = - 14
6r + 15s = 27------ADD
-s = 13
s = - 13

2r = 74
r = 37

c = 37a - 13b

2007-10-04 05:04:06 · answer #1 · answered by Como 7 · 2⤊ 5⤋

7i+9j=r(3i+2j)+s(8i+5j)
so 3r+8s=7 and 2r+5s=9

now it's easy...
you solve the system
you find
r=37 and s= -13

2007-10-04 02:03:45 · answer #2 · answered by Angelique 6 · 1⤊ 2⤋