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Find the Cartesian form the equation of ...

Find the Cartesian form the equation of the plane ` vec r=(s-2t) hat i+(3-t) hat j+(2s+t) hat kdot`

A

`2x-5y-z-15=0`

B

`2x-5y+z-15=0`

C

`2x-5y-z+15=0`

D

`2x+5y-z+15=0`

Text Solution

Verified by Experts

The correct Answer is:
C
Given equation can be rewritten as
`r=3hat(j)+(hat(i)+2hat(k))s(-2hat(i)-hat(j)+hat(k))t`
which is a plane passing through `a=3hat(j)` and parallel to the vectors `b=hat(i)+2hat(k)andc=-2hat(i)-hat(j)+hat(k)` .
Therefore, it is perpendicular to the vector
`n=bxxc=2hat(i)-5hat(j)-hat(k)`
Hence, its vectors equation is `(r-a)*n=0`
`rArr" "r*n=a*n`
`rArr(xhat(i)+yhat(j)+zhat(k))*(2hat(i)-5hat(j)-hat(k))=3hat(j)*(2hat(i)-5hat(j)-hat(k))`
`rArr" "2x-5y-z+15=0`
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