Let `veca` and `vecb` are two given perpendicular vectors, which are non-zero. A vector `vecr` satisfying the equation `vecr xx vecb = veca`, can be

Options

A. `vecb- (vecaxx vecb)/(|vecb|^(2))`
B. `2 vecb - (veca xx vecb)/(|vecb|^(2))`
C. `|veca|vecb- (vecaxxvecb)/(|vecb|^(2))`
D. `|vecb|vecb- (veca xx vecb)/(|vecb|^(2))`

Answer

a,b,cd,

Explanation

since `veca, vecb and veca xx vecb,` are non- coplanar,
`vecr=xveca + yvecb+z(vecaxxvecb)`
`vecr xx vecb = veca`
` Rightarrow xvecaxx vecb + z {(veca.vecb)vecb - (vecb .vecb) veca}= veca`
`- (1+z|vecb|^(2))veca + x vecaxx vecb=0`
`x = 0 and z= 1/(|vecb|^(2))`
Thus, `vecr = y vecb - (vecaxx vecb)/ (|vecb|^(2)) ` where y is the parameter.