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Question

Let the pairs of vectors a,b and c,d each determines 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
Normal vector to plane ¯a,¯b is given by, ¯aׯb
And normal vector to plane ¯c,¯d is given by, ¯cׯd
Now for planes to be parallel, the angle between their normal should be 0 or 180
(¯aׯb)×(¯cׯd)
=|¯aׯb||¯cׯd|sin0
=0

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