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The vector equation of the plane contain...

The vector equation of the plane containing he line `vecr=(-2hati-3hatj+4hatk)+lamda(3hati-2hatj-hatk)` and the point `hati+2hatj+3hatk` is

A

`vecr.(hati+3hatk)=10`

B

`vecr.(hati-3hatk)=10`

C

` vecr.(3hati+hatk)=10`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
The required plane passes through the points `P(-2hati-3hatj+4hatk)` and `Q(hati+2hatj+3hatk)` and is parallel to the vector `vecb=3hati-2hatj-hatk`.
So it is normal to the vector
`vecn=vec(PQ)xxvecb=|(veci,vecj,veck),(-3,-5,1),(3,-2,-1)|=7hati+21hatk`
So, equation of the plane is
`{vecr-(-2hati-3hatj4hatk)}.(7hati+21hatk)=0impliesvecr.(hati+3hatk)=10`
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Knowledge Check

  • The equation of the plane containing the line vecr=hati+hatj+lamda(2hati+hatj+4hatk) is

    A
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    B
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    B
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    C
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