If P×Q=PQ;then what is the angle between P and Q?
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Cross product of two vectors is anti-commutative. That means
(p⃗ ×q⃗ )=−(q⃗ ×p⃗ )
i.e.(p→×q→)=−(q→×p→)
This also means that the angle between (p⃗ ×q⃗ )(p→×q→)and (q⃗ ×p⃗ )(q→×p→) is π or 180∘.
For more explanation-
p×q=pqsin(@) n^
q×p=-pqsin(@) n^
now you think that angle between these two vectors will be 270°, since Sin(@) =-Sin(@) at270°. But it is wrong the actual concept behind this is AT WHAT ANGLE THE VECTORS SHOULD BE IN OPPOSITE DIRECTION.Because this is cross product it is a vector and direction is necessary.
so concluding that
p×q=-q×p
since since direction is opposite hence the angle between the vectors is 180°.
(p⃗ ×q⃗ )=−(q⃗ ×p⃗ )
i.e.(p→×q→)=−(q→×p→)
This also means that the angle between (p⃗ ×q⃗ )(p→×q→)and (q⃗ ×p⃗ )(q→×p→) is π or 180∘.
For more explanation-
p×q=pqsin(@) n^
q×p=-pqsin(@) n^
now you think that angle between these two vectors will be 270°, since Sin(@) =-Sin(@) at270°. But it is wrong the actual concept behind this is AT WHAT ANGLE THE VECTORS SHOULD BE IN OPPOSITE DIRECTION.Because this is cross product it is a vector and direction is necessary.
so concluding that
p×q=-q×p
since since direction is opposite hence the angle between the vectors is 180°.
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