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Find the vector equation of the plane pa...

Find the vector equation of the plane passing through the point having position vector `2hati + 3hatj + 4hatk` and perpendicular to the vector `2hati + hatj -2hatk`.

Text Solution

Verified by Experts

`barr*(2hati + hatj -2hatk) =-1`
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Explore conceptually related problems

Find the vector equation of the plane passing through a point having position vector 3hati - 2hatj + 3hatk and perpendicular to the vector 4hati + 3hatj + 2hatk .

Find the vector equation of the plane passing thrugh a point having position vector 3hati-3hatj+hatk and perpendicular to the vector 4hati+3hatj+2hatk.

Knowledge Check

  • The vector equation of a plane passing through a point having position vector 2hati+3hatj-4hatk and perpendicular to the vector 2hati-hatj+2hatk , is

    A
    `vecr.(2hati-hatj+2hatk)=7`
    B
    `vecr.(2hati-hatj+2hatk)=-7`
    C
    `vecr.(2hati-hatj+2hatk=4`
    D
    none of these

  • The vector eqution of the plane passing through a point having position vector hati-hatj+hatk and parallel to the vectors 2hati+hatj+hatk" and " hatj+2hatk is

    A
    `barr.(hati-4hatj-2hatk)=7`
    B
    `barr.(hati+4hatj+2hatk)=7`
    C
    `barr.(hati-4hatj-2hatk)= -7`
    D
    `barr.(hati-4hatj+2hatk)=7`

  • The vector equation of a line passing through the point with position vector 2hati - hatj - 4hatk and is in the direction of hati - 2hatj + hatk is

    A
    `(2hati - hatj - 4hatk) +lambda(hati - 2hatj + hatk)`
    B
    `(hati +hatj - 5hatk) + lambda(hati - 2hatj + hatk)`
    C
    `(-hati -hatj + 5hatk) + lambda(hati - 2hatj + hatk)`
    D
    `(-2hati + hatj + hatk) + lambda(4hati +hatj + 2hatk)`

    • Similar Questions

    Explore conceptually related problems

    Find the vector equation of a plane passing through a point having position vector (2hati-hatj+hatk) and perpendicular to the vector (4hati+2hatj-3hatk) . Also, reduce it to Cartesian form.

    Find the vector equations of the line passing through the point having positions vector 4 hati -hatj +2hatk and parallel to the vector -2hati -hatj +hatk

    Find the vector equation of the line passing through the point with position vector (hati-2hatj+5hatk) and perpendicular to the plane vecr.(2hati-3hatj-hatk)=0 .

    Find the vector equation of the line passing through the point 2 hati + hatj - 3 hatk and perpendicular to the vectors hati + hatj + hatk and hati + 2 hatj - hatk .

    The componant of vector 2 hati -3 hatj +2hatk perpendicular to the vector hati + -3 hatj + hatk is-

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