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 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)

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) .

Find the equation of the plane which passing through the point hati + hatj + hatk and parallel to the plane vec r.(2hati - hatj + 2hatk) = 0.

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

The line passing through (-1,pi/2) and perpendicular to sqrt3 sin(theta) + 2 cos (theta) = 4/r is

Find the vector equation of the line passing through the point (2,-3,1) and parallel to the planes vec r.(2hati-3hatj-hatk)=3 and vec r.(hati+hatj-hatk)=4 .

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

Find the equation of the plane which passing through the points hati+ hatj+ hatk and parallel to the plane vecr.(2 hati-hatj+2 hatk)=5

The line through hati+3hatj+2hatk and perpendicular to the lines vecr=(hati+2hatj-hatk)+lamda(2hati+hatj+hatk) and vecr=(2hati+6hatj+hatk)+mu(hati+2hatj+3hatk) is

Find the equation of the plane passing through the line of intersection of the planes vec r.(hati+hatj+hatk)=1 and vec r.(2hati+3hatj-hatk)+4=0 and parallel to x-axis.