For example, as shown in the figure,
A ⃗ ⊥ B ⃗ B ⃗ along west
B ⃗ ⊥ C ⃗ A ⃗ along south
C ⃗ along north
A ⃗ . B ⃗ = 0 ∴ A ⃗ . B ⃗ = B ⃗ . C ⃗
B ⃗ . C ⃗ = 0 But B ⃗ ≠ C ⃗

Question

Jitender Pal · Answer

Sol. Give an example for which A ⃗ .B ⃗=C ⃗ .B ⃗ but A ⃗≠C ⃗.

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For example, as shown in the figure, A ⃗ ⊥ B ⃗ B ⃗ along west B ⃗ ⊥ C ⃗ A ⃗ along south C ⃗ along north A ⃗ . B ⃗ = 0 ∴ A ⃗ . B ⃗ = B ⃗ . C ⃗ B ⃗ . C ⃗ = 0 But B ⃗ ≠ C ⃗

For example, as shown in the figure,
A ⃗ ⊥ B ⃗ B ⃗ along west
B ⃗ ⊥ C ⃗ A ⃗ along south
C ⃗ along north
A ⃗ . B ⃗ = 0 ∴ A ⃗ . B ⃗ = B ⃗ . C ⃗
B ⃗ . C ⃗ = 0 But B ⃗ ≠ C ⃗

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For example, as shown in the figure, A ⃗ ⊥ B ⃗ B ⃗ along west B ⃗ ⊥ C ⃗ A ⃗ along south C ⃗ along north A ⃗ . B ⃗ = 0 ∴ A ⃗ . B ⃗ = B ⃗ . C ⃗ B ⃗ . C ⃗ = 0 But B ⃗ ≠ C ⃗

For example, as shown in the figure, A ⃗ ⊥ B ⃗ B ⃗ along west B ⃗ ⊥ C ⃗ A ⃗ along south C ⃗ along north A ⃗ . B ⃗ = 0 ∴ A ⃗ . B ⃗ = B ⃗ . C ⃗ B ⃗ . C ⃗ = 0 But B ⃗ ≠ C ⃗

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For example, as shown in the figure,
A ⃗ ⊥ B ⃗ B ⃗ along west
B ⃗ ⊥ C ⃗ A ⃗ along south
C ⃗ along north
A ⃗ . B ⃗ = 0 ∴ A ⃗ . B ⃗ = B ⃗ . C ⃗
B ⃗ . C ⃗ = 0 But B ⃗ ≠ C ⃗