1.

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

Answer»

`2hat(i)+3hat(j)-3hat(k)`
`2hat(i)+3hat(j)+3hat(k)`
`2hat(i)-5hat(j)+5hat(k)`
`2hat(i)+hat(j)+5hat(k)`

Solution :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`


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