In vectors, if a.b= 0, then either a or b is the zero vector or they are perpendicular. Why can't a and b be both zero vectors to make a.b=0? Why must it be either??
a and b are vectors.
Please explain clearly!
2007-01-19 02:10:16 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
It's not
(either a OR b is the zero vector) or (they are perpendicular).
It's
either [(a or b of the zero vector) OR they are perpendicular].
In other words the "either" applies to the second "or" in the statement, not the first one.
2007-01-19 02:38:18 · answer #1 · answered by Anonymous · 1⤊ 0⤋
Actually, a and b can both be zero vectors. It makes perfect mathematical sense to take the dot product of the zero vector and itself, and the result is zero. i.e., <0,0,0> · <0,0,0> = 0
That is to say, in the statement "a is the zero vector OR b is the zero vector," this is an "inclusive OR," not an "exclusive OR." The OR statement is still satisfied when both elements are true.
2007-01-19 02:14:40 · answer #2 · answered by DavidK93 7 · 1⤊ 0⤋
a.b = (abs value of a) X (abs Value of b) x cos (angle).
If this has to be zero.. one of the three have to be zero.
If both a and b are zero, they dont have a direction and hence, the third portion cannot be determined. And hence, it is said that either a or b has to be zero.
2007-01-19 02:19:16 · answer #3 · answered by RMG 3 · 0⤊ 0⤋
They are perpendicular.
Because they aren't numbers.
They are ordered pairs.
ON THE RIGHT YOU HAVE ZERO NOT ZERO VECTOR.
2007-01-19 02:27:48 · answer #4 · answered by iyiogrenci 6 · 0⤊ 1⤋
Are you sure it says "either a or b" and not just "a or b" ? One is a disjunctive or and the other a conjunctive or. There is a difference.
2007-01-19 02:14:42 · answer #5 · answered by bequalming 5 · 1⤊ 0⤋