Let ` vec a=2 hat i- hat j+ hat k , vec b= hat i+2 hat j= hat ka n d vec c= hat i+ hat j-2 hat k` be three vectors. A vector in the plane of ` vec ba n d vec c` , whose projection on ` vec a` is of magnitude `sqrt(2//3)` , is `2 hat i+3 hat j-3 hat k` b. `2 hat i-3 hat j+3 hat k` c. `-2 hat i- hat j+5 hat k` d. `2 hat i+ hat j+5 hat k`

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`