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Consider the line l : vecr= hati- hatj+ ...

Consider the line `l : vecr= hati- hatj+ hatk+ t(2 hati+3 hatj-6 hatk)` and the plane `p:vecr.(2 hati+3 hatj-6 hatk)=7`.
Statement -I : Then line `l` and the plane 'p' meet in a unique point .
Statement -II: The line `l` is at right angoles to the plane 'p'

A

Statement - I is True, Statement - II is True , Statement - II is a correct explanation for Statement - O

B

Statement- I is True, Statement -II is True , Statement - II is not a correct explanation for Statement - I

C

Statement - I is True, Statement - II is False.

D

Statement - I is False, Statement - II is True.

Text Solution

Verified by Experts

The correct Answer is:
a
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If the line vecr =( hat i-2 hatj + hatk)+t(2 i+ hatj +2 hatk) is parallel to the plane vecr .( 3hat i-2 hatj + mhatk)=14 , Find the value of m.

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Knowledge Check

  • The angle between the line vecr=( hati+2 hatj- hatk)+ lambda( hati- hatj+ hatk) and the plane vecr. (2 hati- hatj+ hatk)=4 is __

    A
    `"cos"^(-1) (1)/(3)`
    B
    `"cos"^(-1) (1)/(sqrt3)`
    C
    0
    D
    `"sin"^(-1) (1)/(3)`
  • If vecA= 5hati+6hatj+3hatk and vecB=6hati-2hatj-6hatk , then

    A
    `vecA and vecB` are perpendicular
    B
    `vecA xxvecB=vecBxxvecA`
    C
    `vecA and vecB` have the same magnitude
    D
    `vecA*vecB=0`
  • If the line vecr=(2hati-hatj+3hatk)+lambda(2hati+hatj+2hatk) is parallel to the plane vecr*(3hati-2hatj+p hatk)=4 then the value of p is -

    A
    2
    B
    -2
    C
    3
    D
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