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Distance of point P( vec p) from the pla...

Distance of point `P( vec p)` from the plane ` vec rdot vec n=0` is a. `| vec pdot vec n|` b. `(| vec pxx vec n|)/(| vec n|)` c. `(| vec pdot vec n|)/(| vec n|)` d. none of these

A

`|vecp.vecn|`

B

`(|vecpxxvecn|)/(|vecn|)`

C

`(|vecp.vecn|)/(|vecn|)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
c
Let `Q(vecq)` be the foot of altitude drawn from P to
the plane `vecr.vecn=0`. Then
`vecq-vecp=lamdavecnorvecq=vecp+lamdavecn`
Also `vecq.vecn=0implies(vecp+lamdavecn).=0`
or `lamda=-(vecp.vecn)/(|vecn|^(2))orvecq-vecp=-(vecp.vecn)/(|vecn|^(2))vecn`
Thus, required distance `=|vecq-vecp|=(|vecp.vecn|)/(|vecn|)=(|vecp.vecn|)`
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