Let `a=2hat(i)-hat(j)+hat(k), b=hat(i)+2hat(j)-hat(k)` and `c=hat(i)+hat(j)-2hat(k)` be three vectors, A vector in the plane of b and c whose projection on a is of magnitude `sqrt(2/3)`, is

Options

A. `2hat(i)+3hat(j)-3hat(k)`
B. `2hat(i)+3hat(j)+3hat(k)`
C. `2hat(i)-5hat(j)+5hat(k)`
D. `2hat(i)+hat(j)+5hat(k)`

Answer

A

Explanation

Any vector I the place of b and c is
`r=mb+c(m+1)hati+(2m+1)hati+(-m-2)hatk`
Projection of r on a `=(r*a)/(|a|)=|sqrt(2/3)|`
`:." "(2(m+1)-(2m+1)+(-m-2))/(sqrt6)=+-sqrt(2/3)`
`rArr" "-m-2+-2rArrm=-3"and"1`
Hence, `r=-2hati-5hatj+hatk" and "r=2hati+3hatj-3hatk`