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The equation of the plane passing throug...

The equation of the plane passing through the point `(2, -1, 3)` and perpendicular to the vector `3hati + 2hatj - hatk` is

A

`barr*(3hati+2hatj-hatk)=1`

B

`barr*(3hati+2hatj-hatk)+1 =0`

C

`barr*(3hati+2hatj-hatk) =0`

D

`barr*(3hati+2hatj+hatk) =1`

Text Solution

Verified by Experts

The correct Answer is:
A
`barr*(3hati + 2hatj - hatk) = 1`
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Find Cartesian equations of the line passing through the point A(2,1,-3) and perpendicular to vectors hati +hatj + hatk and hati +2hatj -hatk

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Knowledge Check

  • The vector equation of a line passing through the point hati + 2hatj + 3hatk and perpendicular to the vectors hati +hatj + hatk and 2hati - hatj + hatk is

    A
    `(hati + 2hatj + 3hatk) + lambda(-2hati - hatj + 3hatk)`
    B
    `(hati + 2hatj + 3hatk) + lambda(2hati + hatj - hatk)`
    C
    `(hati + 2hatj + 3hatk) +lambda(2hati + hatj - hatk)`
    D
    `(hati + 2hatj + 3hatk) + lambda(2hati - hatj - 2hatk)`

  • The equation of a line passing through the point (4,-2,5) and parallel to the vector 3hati -hatj + 2hatk is

    A
    `(x-4)/3 = (y+2)/-1 = (z-5)/2`
    B
    `(x+4)/3 = (y-2)/-1 = (z+5)/2`
    C
    `(x-3)/4 = (y+1)/-2 = (z-2)/5`
    D
    `(x+3)/4 = (y-1)/-2 = (z+2)/5`

  • The vector equation of the plane passing through the point (-1, 2,-5) and parallel to the vectors 4hati-hatj+3hatk and hati+hatj-hatk is

    A
    `vecr.(-2hati+7hatj+5hatk)=13`
    B
    `vecr.(-2hati+7hatj+5hatk)=-13`
    C
    `vecr.(-2hati+7hatj+5hatk)=-9`
    D
    `vecr.(-2hati+7hatj+5hatk)=9`

    • Similar Questions

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    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 .

    Find the vector and cartesian equations of the plane that passes through the point (0, 1, -2) and normal to the vector hati + hatj + hatk .

    Find the equation of a line passing through the point (1,2,3) and perpendicular to the plane vecr.(2hati-3hatj+4hatk) = 1 .

    Find the Cartesian equation of the plane passing through point A(1, 2, 3) and which is perpendicular to a vector vecn=2hati-3hatj+4hatk

    Find the vector equation of a line passing through the point A(1,-1,2) and perpendicular to the plane vecr.(2hati-hatj+3hatk)=5 .

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