Dot product of two vectors `overset(rarr)A` and `overset(rarr)B` is defined as `overset(rarr)A.overset(rarr)B=aB cos phi` , where `phi` is 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)A` that . 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)B` also called the cross product, is denoted by `overset(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)B` then `C=AB sin theta` ,
For non zero vectors `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

Options

A. `overset(rarr)A.overset(rarr)B=0,overset(rarr)B.overset(rarr)C=0`
B. `overset(rarr)B.overset(rarr)C=0,overset(rarr)C.overset(rarr)A=0`
C. `overset(rarr)C.overset(rarr)A=0,overset(rarr)A.overset(rarr)B=0`
D. `overset(rarr)A.overset(rarr)B=overset(rarr)B.overset(rarr)C=overset(rarr)C.overset(rarr)A=0`

Answer

d

Explanation

`(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`