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in Vector algebra by (36.3k points)

If a, b, c and d are unit vectors such that (a × b).(c × d) = 1 and (a × c) = 1/2, then 

(a) a, b, c are non-coplanar 

(b) b, c, d are non-coplanar 

(c) b, d are non-parallel 

(d) a, d are parallel and b, c are parallel

1 Answer

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by (33.0k points)
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Best answer

Answer is (c) b and d are non-parallel

Explanation:

Let θ1 and θ2 be the angles between a and b, and c and d and n1 and n2 are the unit vectors perpendicular to the plane of a and b, and c and d.

Now,

Since the angle between a and c is π/3 and b and d is also π/3. So b and d are non-parallel.

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