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Perpendicular vectors True/False watch

1. Given three nonzero vectors a, b and c, are the following statements True or False? Give a short reason or counter-example to justify your answer.
(a) If a ⊥ b and also b ⊥ c then a ⊥ c.
(b) If a ⊥ b and also a ⊥ c then a ⊥ (b + c).
(c) If a ⊥ b and also b ⊥ c then b ⊥ (a − c).
(d) If a ⊥ (b + c) and also a ⊥ (b − c) then a ⊥ b.

a. true
A=ax i + ay j + az k
C=cx i + cy j + cz k

if (ax)(cx)+(ay)(cy)+(az)(cz) = 0 then A⊥C

^i think
2. Picture a bicycle wheel, and let "a" be one of the spokes and "b" the axle. "a" is perpendicular to "b". Now let "c" be another of the spokes. The axle "b" is perpendicular to all the spokes "c", but most of the spokes "c" are not perpendicular to the initial spoke "a".

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Updated: February 8, 2018
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