Let →a, →b and →c be three unit vectors, out of which vectors →b and →c are non-parallel. If α and β are the angles which vector →a makes with vectors →b and →c respectively and →a × (→b × →c) = 12→b, then |α − β| is equal to:

→a × (→b × →c) = (→a . →c)→b − (→a . →b)→c = 12→b
Since →b and →c are linearly independent, we have:
(→a . →c)→b − (→a . →b)→c = 12→b
Comparing the coefficients of →b and →c, we get:
→a . →c = 12
→a . →b = 0
(All given vectors are unit vectors)
Since →a and →b are unit vectors, and →a . →b = 0, the angle between →a and →b is 90°. Thus α = 90°.
Since →a and →c are unit vectors, and →a . →c = 12, we have cos β = 12, which implies β = 0°.
Therefore, |α − β| = |90° − 0°| = 90°.
However, there seems to be a mistake in the given solution. Let's reconsider the problem.
→a × (→b × →c) = (→a . →c)→b − (→a . →b)→c = 12→b
Since →b and →c are linearly independent, we can equate the coefficients:
→a . →c = 12
→a . →b = 0
Since →a, →b, →c are unit vectors, we have:
→a . →b = |→a||→b|cos α = cos α = 0 => α = 90°
→a . →c = |→a||→c|cos β = cos β = 12
This is not possible since |cos β| ≤ 1. There must be a mistake in the question or the given solution. Let's assume the given equation is:
→a × (→b × →c) = 12→b
Using the vector triple product identity, we have:
→a × (→b × →c) = (→a . →c)→b − (→a . →b)→c = 12→b
Comparing coefficients, we get:
→a . →c = 12
→a . →b = 0
Since |→a| = |→b| = |→c| = 1, we have:
cos β = 12 (This is incorrect as |cos β| ≤ 1)
cos α = 0 => α = 90°
Let's assume there was a mistake in the problem statement and the equation should have been →a × (→b × →c) = →b. Then →a . →c = 1 and →a . →b = 0. This gives α = 90° and β = 0°. Then |α - β| = 90°. This is not among the options. There is an inconsistency in the problem statement.