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Question

A parallelogram is constructed on the vectors ¯α and ¯β. A vector which coincides with the altitude of the parallelogram and perpendicular to the side ¯α expressed in terms of the vectors ¯α and ¯β is

A
¯β+¯β¯α(¯α)2¯α
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B
(¯αׯβ)ׯα(¯α)2
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C
¯β¯α(α)2¯α+¯β
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D
¯β¯α×(¯αׯβ)(α)2
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Solution

The correct option is B (¯αׯβ)ׯα(¯α)2
(α×β) will give us the perpendicular vector or the normal to the plane where the parallelogram is lying.

Now
(α×β)×α will give the vector parallel to the altitude of the parallelogram which is perpendicular to side ¯α.

Thus the unit vector of the altitude of the given parallelogram perpendicular to ¯α will be
=(α×β)×α|α|2

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