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The equation of the plane perpendicular ...

The equation of the plane perpendicular to the line `(x-1)/1=(y-2)/(-1)=(z+1)/2` and passing through the point (2,3,1), is

A

`r*(hat(i)+hat(j)+2hat(k))=1`

B

`r*(hat(i)-hat(j)-2hat(k))=1`

C

`r*(hat(i)-hat(j)-2hat(k))=7`

D

`r*(hat(i)+hat(j)+2hat(k))=10`

Text Solution

Verified by Experts

The correct Answer is:
B
Given line is parallel to vector `n=hat(i)-hat(j)+2hat(k)`. The required plane passing through the point (2,3,1) i.e.
`2hat(i)+3hat(k)+hat(k)` and is perpendicular to the vector
`n=hat(i)-hat(j)+2hat(k)`
`:.` Its equation is
`[(r-(2hat(i)+3hat(j)+hat(k)))]*(hat(i)-hat(j)+2hat(k))=0`
`rArr" "r*(hat(i)-hat(j)+2hat(k))=1`
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