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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:

Answer

Step by step text solution for 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: by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

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Find the equation of a line passing through the point P(2,-1,3) and perpendicular to the lines vecr=(hati+hatj-hatk)+lambda(2hati-2hatj+hatk) and vec r=(2hati-hatj-3hatk)+mu(hati+2hatj+2hatk) .

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Knowledge Check

  • 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 lt t lt oo l_(2) : (3 + 2s) hat(i) + (3 + 2s) hat(j) + (2 + s)hat(k), -oo lt s lt oo Then the coordinate (s) of the point (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))`

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

    A
    `vecr=2hati-3hatj+4hatk+lambda(3hati-hatj+2hatk)`
    B
    `vecr=-3hati+hatj-2hatk+lambda(2hati-3hatj+4hatk)`
    C
    `r=3hati-hatj+2hatk+lambda(hati+2hatj-2hatk)`
    D
    `vecr=3hati-hatj+2hatk+lambda(2hati-3hatj+4hatk)` where `lambda` is a scalar

  • A vector perpendicular to both of (3hati+hatj+2hatk) and (2hati-2hatj+4hatk) is

    A
    `1/(sqrt(3))(hati+hatj-hatk)`
    B
    `hati-hatj-hatk`
    C
    `1/(sqrt(3))(hati+hatj+hatk)`
    D
    `(sqrt(3)hati-hatj-hatk)`

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