Dot product of two vectors overset(rarr)A and overset(rarr)Bis defined as overset(rarr)A.overset(rarr)B=aB cos phi, where phiis angle between them when they are drawn with tails coinciding. For any two vectors. This means ovsert(rarr)A . overset(rarr)B=overset(rarr)B. overset(rarr)Athat. The scalar product obeys the commutative law of multiplication, the order of the two vectors does not matter. The vector product of two vectors overset(rarr)A and overset(rarr)Balso called the cross product, is denoted byoverset(rarr)A xx overset(rarr)B . As the name suggests, the vector product is itself a vector. overset(rarr)C=overset(rarr)A xx overset(rarr)Bthen C=AB sin theta, For non zerovectors overset(rarr)A, overset(rarr)B, overset(rarr)C,|(overset(rarr)Axxoverset(rarr)B).overset(rarr)C|=|overset(rarr)A||overset(rarr)B||overset(rarr)C| holds if and only if

Dot product of two vectors overset(rarr)A and overset(rarr)Bis defined

1.	Dot product of two vectors overset(rarr)A and overset(rarr)Bis defined as overset(rarr)A.overset(rarr)B=aB cos phi, where phiis angle between them when they are drawn with tails coinciding. For any two vectors. This means ovsert(rarr)A . overset(rarr)B=overset(rarr)B. overset(rarr)Athat. The scalar product obeys the commutative law of multiplication, the order of the two vectors does not matter. The vector product of two vectors overset(rarr)A and overset(rarr)Balso called the cross product, is denoted byoverset(rarr)A xx overset(rarr)B . As the name suggests, the vector product is itself a vector. overset(rarr)C=overset(rarr)A xx overset(rarr)Bthen C=AB sin theta, For non zerovectors overset(rarr)A, overset(rarr)B, overset(rarr)C,\|(overset(rarr)Axxoverset(rarr)B).overset(rarr)C\|=\|overset(rarr)A\|\|overset(rarr)B\|\|overset(rarr)C\| holds if and only if
Answer» `overset(rarr)A.overset(rarr)B=0,overset(rarr)B.overset(rarr)C=0` `overset(rarr)B.overset(rarr)C=0,overset(rarr)C.overset(rarr)A=0` `overset(rarr)C.overset(rarr)A=0,overset(rarr)A.overset(rarr)B=0` `overset(rarr)A.overset(rarr)B=overset(rarr)B.overset(rarr)C=overset(rarr)C.overset(rarr)A=0` Solution :`(AB sin theta ) C COS phi =ABC sin theta cos phi =1 rarr "that" =90^(@)` and `phi` =0 i.e `barA ,BARB` and `barc` are mutually perpendicular `barA.barB=barB .barC.barA=0`

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