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Find the distance between the planes r*(...

Find the distance between the planes `r*(2hat(i)-hat(j)+3hat(k))=4andr*(6hat(i)-3hat(j)+9hat(k))+13=0`

A

`(5)/(3(sqrt(14)))`

B

`(10)/(3(sqrt(14)))`

C

`(25)/(3(sqrt(14)))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Given, planes are
`r*(2hat(i)-hat(j)+3hat(k))-4=0`
`and" "r*(2hat(i)-hat(j)+3hat(k))+(13)/(3)=0`
Here we see that `n_(1)=n_(2)`
so, they are parallel to each other.
`:.` Required distance
`=(|{:(13)/(3)+4:}|)/(sqrt(2/^(2)+(-1)^(2)+(3)^(2)))=(25)/(3sqrt(14))`
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