Find the length of the perpendicular drawn from the point`(5,4,-1)` to the line ` vec r= hat i+lambda(2 hat i+9 hat j+5 hat k),` wher `lambda` is a parameter.

Find the length of the perpendicular drawn from the point (5,4,-1) .to the line vec r=hat i+lambda(2hat i+9hat j+5hat k)

Find the co-ordinates of the foot of perpendicular and the length of the perpendicular drawn from the point P (5,4,2) to the line : vec(r) = hati + 3 hat(j) + hat(k) + lambda ( 2 hat(i) + 3 hatj - hatk ) . Also, find the image of P in this line.

The length of the perpendicular drawn from the point (2,1,4) to the plane containing the lines vec r=(hat i+hat j)+lambda(hat i+2hat j-hat k) and vec r=(hat i+hat j)+mu(-hat i+hat j-2hat k) is:

Find the foot of the perpendicular drawn from the point 2hat i-hat j+5hat k to the line vec r=(11hat i-2hat j-8hat k)+lambda(10hat i-4hat j-11hat k) Also find the length of the perpendicular.

The image of the point (1,2,3) about the line vec r=(2hat i+3hat j-hat k)+lambda(hat i2hat j+2hat k) is

The length of the perpendicular from the point with position vector hat i+2hat j+3hat k the line vec r=(3hat i+4hat j-3hat k)lambda(2hat i-3hat j+6hat k) is

Find the equation of the plane passing through the point (1,1,1) and containing the line vec r=(-3hat i+hat j+5hat k+)lambda(3hat i-hat j-5hat k) Also,show that the plane contains the lines vec r=(-hat i+2hat j+5hat k)+lambda(hat i-2hat j-5hat k)

Find the equation of the plane passing through the point (1,1,1) and containing the line vec r=(-3hat i+hat j+5hat k)+lambda(3hat i-hat j5hat k) Also,show that the plane contains the lines vec r=(-hat i+2hat j+5hat k)+lambda(hat i2hat j5hat k)

Find the equation of a line passing through a point (2, -1, 3) and parallel to the line -> r=( hat i+ hat j)+lambda(2 hat i+ hat j-2 hat k)dot

Find the distance of the point (-1,-5,-10) from the point of intersection of the line vec r=2hat i-hat j+2hat k+lambda(3hat i+4hat j+2hat k) and the plane vec r*(hat i-hat j+hat k)=5