# Vectors QuestionWatch

#1
I'm having a bit of trouble with a vectors question and would really appreciate some help. "Three distinct non-zero vectors are given by OA = a, OB = b, and OC = c. If OA is perpendicular to BC and OB is perpendicular to CA, show that OC is perpendicular to AB."

Since OA is perpendicular to BC, a(c - b) = 0 ? ac - ab = 0

Since OB is perpendicular to CA, b(a - c) = 0 ? ba - bc = 0

Simultaneous equations:

ac - ab = 0
ba - bc = 0

- ab + ac = 0
ba - bc = 0

It's obvious that we get ac - bc = 0 ? c(a - b) = 0 ? so OC is perpendicular to AB.

But what I don't understand is how the -ab and ba vectors "cancel out". Doesn't it become -ab and ba = ba + ba = 2ba ? Or am I missing a trick here?
0
7 years ago
#2
You mean a.(c-b)= 0 so a.c - a.b=0
and b.(a-c)=0 so b.a - b.c=0

Note the a.b = b.a these are scalar quantities not vectors
1
#3
(Original post by vc94)
You mean a.(c-b)= 0 so a.c - a.b=0
and b.(a-c)=0 so b.a - b.c=0

Note the a.b = b.a these are scalar quantities not vectors
Oh yeah, forgot about that... thanks
1
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