OX = nOQ
If OX = ma + b - ab and OQ = 4a + 2b
(a and b being vectors) clearly show how n = 1/6 and m = 2/3
2006-08-31 06:17:33 · 2 answers · asked by MO 2 in Science & Mathematics ➔ Mathematics
OX = nOQ
If OX = ma + b - mb and OQ = 4a +2b
(a and b being vectors) find the value of n and m.
NB: n = 1/6 and m = 2/3
Show me how to work it out.
2006-08-31 06:23:04 · update #1
Let OX=nOQ, then OX-nOQ=0
replace OX and OQ with theirs representation in vectors a, b (OX=ma+b-mb, OQ=4a+2b).
You receive:
ma+b-mb-n(4a+2b)=0 or the same:
ma+b-mb-4na-2nb=0.
Collect coefficients at a and b:
(m-4n)a+(1-m-2n)b=0
If a and b are lineary independent not null vectors, then the left side can be equal to 0 only if the both coeffitients at the a and b equal to 0. Thus:
m-4n=0
1-m-2n=0
Its an equation system. Solving...
m=1-2n
1-2n-4n=0->
1-6n=0->
n=1/6
m=1-2*1/6=2/3
Happy End!!!
2006-08-31 07:57:23 · answer #1 · answered by sav 2 · 0⤊ 0⤋
Is this what you want?
2006-08-31 13:23:31 · answer #2 · answered by Anonymous · 0⤊ 0⤋