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

Options

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

Answer

A, B, C, D

Explanation

Since, `veca , vecb` and `veca xx vecb` are non-coplanar.
So, `vecr = xveca + yvecb+z(veca xx vecb)`
Given, `vecr xx vecb=veca`
`rArr xveca xx vecb + z{(veca.vecb)vecb-(vecb.vecb)veca}=veca`
`rArr -(1+z|vecb|^(2))veca + xveca xx vecb=0["since"veca.vecb=0]`
`x=0` and `z=-1/|vecb|^(2)`
Thus, `vecr = yvecb-(veca xx vecb)/(|vecb|)`, where y is the parameter.