Let `vecx,vecy and vecz` be three vector each of magnitude `sqrt(2)` and the angle between each pair of them is `(pi)/(3).` if `vcea` is a non - zero vector perpendicular to `vecx and vecy xxvecz and vecb` is a non-zero vector perpendicular to `vecy and vecz xx vecx,` then

Options

A. `vecb= (vecb.vecz) (vecz-vecx) `
B. `veca= (veca.vecy)(vecy - vecz)`
C. `veca.vecb=-(veca.vecy) (vecb.vecz)`
D. `veca= (veca.vecy)(vecz- vecy)`

Answer

a,b,c

Explanation

Accoding to the question
` vecx. Vecz = vecx .vecy =vecy.vecz=sqrt2.sqrt2. cos " " pi/3=1 `
Given `veca` is perpendicular to `vecx and vecy xx vecz`
`veca = lamda_(1)((vecx.vecz) vecy- (vecx .vecy) vecz)`
` Rightarrow veca = lamda _(1) (vecy -vecz)`
Now, `veca. vecy =lamda_(1) (vecy. vecy.vecz) = lamda_(1)(2-1)`
` Rightarrow lamda_(1) = veca. vecy`
From (1) and )(2), `veca. (veca.vecy)(vecy-vecz)`
Similarly, `vecb= (vecb.vecz) (vecz-vecx)`
Now `veca.vecb= (veca.vecy) (vecb.vecz) [(vecy-vecz).(vecz-vecx)]`
`= (veca.vecy) (vecb.vecz) [ 1-2+1]`
` =- (veca.vecy) (vecb.vecb.vecz)`