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The direction cosines of the perpendicul...

The direction cosines of the perpendicular from the origin to the plane `vecr.(6hati-3hatj-2hatk)+1=0` are

A

`6/7,3/7,-2/7`

B

`6/7,-3/7,2/7`

C

`-6/7,3/7,2/7`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
c
Given planes is `vecr.(-6hati+3hatj+2hatk)=1`.
`therefore vecr.vecn=p`, where `vecn=(-6hati+3hatj+2hatk)`.
D.r.'s of the normal to the given plane are `-6,3,2` and `sqrt((-6)^(2)+3^(2)+2^(2))=sqrt(49)=7`.
`therefore` d.c's of the normal to the given plane ar e`-6/7, 3/7,2/7`.
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Find the direction cosines of the perpendicular from the origin to the plane vecr.(6hati-3hatj-2hatk)+1=0 .

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Knowledge Check

  • The direaction cosines of perpendicular from orgin to the plane barr.(2hati+3hatj+6hatk)+7=0 are

    A
    `(-2)/(7),(-3)/(7),(-6)/(7)`
    B
    `(2)/(7),(3)/(7),(6)/(7)`
    C
    `(2)/(7),(-3)/(7),(6)/(7)`
    D
    `(2)/(7),(-3)/(7),(-6)/(7)`

  • The length of perpendicular from the origin to the plane vecr.(-3hati-4hatj-12hatk)+39=0 is

    A
    3 units
    B
    `13/5` units
    C
    `5/3` units
    D
    none of these

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