Question #88d58

1 Answer
Hari O.
May 15, 2017

Zero.

Explanation:

This is one case of Scalar triple product :-

# A.(B # x # C)#

Geometrically #A, B, C# are the there vectors defining there sides of a parallelepiped.
and the scalar triple product of these vectors give it's volume.

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So now to evaluate, (#C # x # D#)#.##D#

When we evaluate, #C # x # D#, we get a vector(lets say #A)# which is perpendicular to vector #C# and #D#.

And finding the dot product of #A#.#D#, we get,

#A#.#D#=#|A|##|D|##cos90#--------( #cos90# because #A# is perpendicular to #D#)

we know #cos90##=##0#.

So, #A#.#D##=##0#.

#rArr# (#C # x # D#)#.##D# #=# #0#

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