For non-zero vectors `veca, vecb and vecc , |(veca xx vecb) .vecc = |veca||vecb||vecc|` holds if and only if

Options

A. `veca.vecb=0 , vecb .vecc=0`
B. `vecb.vecc = 0, vecc, veca =0`
C. `vecc.veca =0, veca,vecb =0`
D. `veca.vecb= vecb.vecc= vecc.veca =0`

Answer

d

Explanation

`|(veca xx vecb).vecc|=|veca||vecb||vecc|`
`or||veca||vecb|sin theta cos alpha|=|veca||vecb||vecc|`
` or |sinstheta||cos alpha|=1`
`Rightarrow theta=pi//2 and alpha=0`
` Rightarrow veca bot vecband vecc||hatn`
or perpendicular to both `veca and vecb`
`Rightarrow veca.vecb=vecb.vecc=vecc.veca=0`