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A line l passing through the origin is p...

A line `l` passing through the origin is perpendicular to the lines `l_1: (3+t)hati+(-1+2t)hatj+(4+2t)hatk , oo < t < oo , l_2: (3+s)hati+(3+2s)hatj+(2+s)hatk , oo < t < oo` then the coordinates of the point on `l_2` at a distance of `sqrt17` from the point of intersection of `l&l_1` is/are:

A

`((7)/(3), (7)/(3), (5)/(3))`

B

`(-1, -1, 0)`

C

`(1, 1, 1)`

D

`((7)/(9), (7)/(9), (8)/(9))`

Text Solution

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The correct Answer is:
B, D
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A line l passing through the origin is perpendicular to the lines l_(1):(3+t)hat i+(-1+2t)hat j+(4+2t)hat k,oo

A line 'l' passing through origin is perpendicular to the lines l_1:vecr=(3+t)hati+(-1+2t)hatj+(4+2t)hatk l_2:vecr=(3+2s)hati+(3+2s)hatj+(2+s)hatk If the co - ordinates of the point in the first octant on 'l_(2)' at a distance of sqrt(17) from the point of intersection of 'l' and 'l'_1 are (a,b,c) , then 18 (a + b + c) is equal to

Knowledge Check

  • A line l passing through the origin is perpendicular to the lines l_1:(3+t)hati+(-1+2t)hatj+(4+2t)hatk,-infty lt t lt infty l_2:(3+2s)hati+(3+2s)hatj+(2+s)hatk,-infty lt g lt infty Then, the coordinate(s) of the points(s) on l_2 at a distance of sqrt17 from the point of intersection of l and l_1 is (are)

    A
    `(7/3,7/3,5/3)`
    B
    (-1,-1,0)
    C
    (1,1,1)
    D
    `(7/9,7/9,8/9)`

  • A line l passing through the origin is perpendicular to the lines 1: (3 + t ) hati + (-1 +2 t ) hatj + (4 + 2t) hatk -oolt t lt ooand 1__(2) : (3 + 2s )hati + (3+2s) hati + (3+ 2s) hatj + ( 2+s) hatk , -oo lt s lt oo Then the coordinate(s) of the point(s) on 1 _(2) at a distance of sqrt17 from the point of intersection of 1 and 1_(1) is (are)

    A
    `((7)/(3), (7)/(3), (5)/(3))`
    B
    `(-1,-1,0)`
    C
    `(1,1,1)`
    D
    `((7)/(9), (7)/(9), (8)/(9))`

  • 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`

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    Find the vector equation of the line through the origin, which is perpendicular to the plane vec(r) . (hati - 2 hatj + hatk) = 3 .

    Find the vector equation of a lie passing through the origin perpendicular to the plane vecr.(hati+2hatj+3hatk)=3 .

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

    Find the vector equationof the line passing through the point (3,1,2) and perpendicular to the plane vecr.(2hati-hatj+hatk)=4 . Find also the point of intersection of this line and the plane.

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