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 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)

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 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.

Find the equation of the plane passing through the point hati-hatj+hatk and perpendicular to the vectro 3hati-hatj-2hatk and show that the point 2hati+4hatj lies on the plane.

Find the equation of a plane passing through origin and which is perpendicular to a normal vector 2hati+ hatj -hatk . (Cartesian form )

Find the equation of the line which passes through the point (-1,3,-2) and is perpendicular to the lines (x)/(1)=(y)/(2)=(z)/(3) and vecr=(-2hati+hatj-hatk)+lamda(-3hati+2hatj+5hatk) .

If a line passing through (-2, 1, alpha) and (4, 1, 2) is perpendicular to the vector 3hati-4hatj+5hatk and parallel to the plane containing vectors hati+2betahatk and 2beta hati+alpha hatk(AA beta ne 0), then 10(alpha+beta) is equal to

The line passing through (-4, -2) and (2, -3) is perpendicular to the line passing through (a, 5) and (2, -1). Find a.

The area (in square units ) of the triangle formed by y-axis , the straight line L passing through (1,1) and (2,0) and the straight line perpendicular to the line L and passing through (1/2, 0) , is

In the accompanying figure. Line l passes through the origin and the point (2, 4). Line m (not shown) is perpendicular to line l at (2, 4). Line m intersects the x-axis at which point?