1.

Let a=hati+2hatj+hatk, b=hati-hatj+hatk and c=hati+hatj-hatk. A vector in the plane a and b whose projection on c is (1)/(sqrt3), is

Answer»

`HATI+hatj-2hatk`
`3hati+hatj-3hatk`
`4hati-hatj+4hatk`
`4hati+hatj-4hatk`

SOLUTION :Any vector R in the plane containing a and b is `a + lambda b`
`thereforer = ( hati + 2 hatj + HATK ) + lambda(hati-hatj+hatk)`
`=(1+lambda)hati + (2 -lambda)hatj + (1+lambda)hatk`
PROJECTION of r on `c=(r*c)/(|c|)`
`rArr ([(1+lambda)hati+(2-lambda)hatj+(1+lambda)hatk]*(hati+hatj-hatk))/(sqrt((1)^(2)+(1)^(2)+(-1)^(2)))=|(1)/(sqrt(3))|`
`rArr (1+lambda + 2 -lambda - 1-lambda)/(sqrt(3))=|(1)/(sqrt(3))|`
`rArr2-lambda = pm 1 rArr lambda 1,3 `
`thereforer = 2 hati +hatj + 2 hatk , 4 hati -hatj + 4 hatk`


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