The vector equation of plane which is at a distance of 8 unit from the origin and which is normal to the vector `2hat(i)+hat(j)+2hat(k)` is `r*(2hat(i)+hat(j)+2hat(k))=lamda`, where `lamda` is equal to

Options

A. 0
B. 24
C. 42
D. 8

Answer

B

Explanation

Here, `d=8,n=2hat(i)+hat(j)+2hat(k)`
`hat(n)=(n)/(|n|)=(2hat(i)+hat(j)+2hat(k))/(sqrt(4+1+4))=(1)/(3)(2hat(i)+hat(j)+2hat(k))`
Hence, the required equation of plane is `r*hat(n)=d`
`rArr" "r*(2hat(i)+hat(j)+2hat(k))/(3)=8`
`rArr" "r*(2hat(i)+hat(j)+2hat(k))=24`
Hence, `lamda=24`