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 `veca` 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
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)`
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The correct Answer is:
A, B, C
a,,b., c. According to the question `vecx.vecz=vecx.vecy=vecy.vecz=sqrt(2).sqrt(2). cos ""(pi)/(3)=1` Given `veca` is perpendicular to `vecx and vecyxxvecz` `therefore veca =lamda_(1)(vecx xx(vecyxx vecz))` `implies veca=lamda_(1) ((vecx.vecz)vecY-(vecx . vecy)vecz)` `implies veca=lamda_(1) (vecy-vecz)` Now` veca. vecy = lamda _(1) ( vecy. vecy- vecy.vecz) = lamda_(1) (2-1) ` ` implies lamda_(1) = veca . vecy` From (1) and (2) , `veca= ( veca. vecy) ( vecy- vexz)` Similarly , ` vecb = ( vecb. vecz)( vecz - vecx) ` Now , `veca. vecb =(vecb. vecz) [ ( vecy-vecz).( vecz- vecx)]` `= ( veca . vecy) (vecb. vecz) [1-1-2+1]` ` =- ( veca. vecy) ( vecb. vecz) `
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CENGAGE-JEE 2019-chapter -2 multiple correct answers type
