Let PQ be a line segment with `P(x_1, y_1, z_1) and Q(x_2, y_2, z_2)` and let L. be a straight line whose d.c.'s are l, m, n. Then the length of projection of PQ on the line L is

Distance of the point P(x_2, y_2, z_2) from the line (x-x_1)/l=(y-y_1)/m=(z-z_1)/n , where l,m,n are the direction cosines of the line, is

If the straight line L=3x+4y-k=0 cuts the line segment joining the points P(2,-1) and Q(1,1) in the ratio 4:1 , then the equation of the line parallel to the line y=x and concurrent with the lines PQ and L =0 is

(b)The coordinates of the point R which divides the line segment joining P(x1,y1,z1) and Q(x2,y2,z2) internally in the ratio m:n are given by…………

Consider the line L : (x-1)/(2) = (y)/(1) = (z+1)/(-2) and a point A (1,1,1). Let P be the foot of the perpendicular from A on L and Q be the image of the point A in the line L, 'O' being the origin. The distance of the origin from the plane passing through the point A and containing the line L is

Consider the line L : (x-1)/(2) = (y)/(1) = (z+1)/(-2) and a point A (1,1,1). Let P be the foot of the perpendicular from A on L and Q be the image of the point A in the line L, 'O' being the origin. The distance of the point A from the line L is

Let C : x^(2) -3, D : y = kx^(2) be two parabolas and L_(1) : x a , L_(2) : x = 1 (a ne 0) be two straight lines. IF the line L_(1) meets the parabola C at a point B on the line L_(2) , other than A, then a may be equal to

Consider the line L : (x-1)/(2) = (y)/(1) = (z+1)/(-2) and a point A (1,1,1). Let P be the foot of the perpendicular from A on L and Q be the image of the point A in the line L, 'O' being the origin. The distance of the origin from the point Q is

If l,m,n be d.cs, of a line ,then the line is perpendicular to the plane x-3y+2z+1=0 if ______.