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Question

Let the pairs a,b and c,d each determine a plane, then the planes are parallel if

A
(a×c)×(b×d)=0
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B
(a×c)(b×d)=0
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C
(a×b)×(c×d)=0
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D
(a×b)(c×d)=0
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Solution

The correct option is C (a×b)×(c×d)=0
a×b is a vector perpendicular to the plane contining a and b.

Similarly, c×d is a vector perpendicular to the plane containing c and d.

Thus, the two planes will be parallel if their normals,
i.e., a×b and c×d, are parallel.

Thus,
(a×b)×(c×d)=0

Hence, option C.

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