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)dot`

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 coordinates of the foot of the perpendicular and the length of the perpendicular drawn from the point P(5,4,2) to the line vec(r) = -hat(i) + 3hat(j) + hat(k) + lambda (2hat(i) + 3hat(j) - hat(k)) .

Fine the equation of the perpendicular drawn from the point P(-1,\ 3,\ 2) to the line -> r=(2 hat j+3 hat k)+lambda( hat i+2 hat j+3 hat k)dot Also find the coordinates of the foot of the perpendicular from Pdot

Find the foot of the perpendicular drawn from the point hat i+6 hat j+3 hat k to the line vec r= hat j+2 hat k+lambda( hat i+2 hat j+3 hat k)dot Also, find the length of the perpendicular.

Find the length and the foot of the perpendicular from the point (1, 1, 2) to the plane vec rdot(( hat i-2 hat j+4 hat k)+5=0.

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

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

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

Find the equation of the line passing through the point hat i+ hat j- hat k and perpendicular to the lines vec r= hat i+lambda(2 hat i+ hat j-3 hat k)a n d vec r=(2 hat i+ hat j- hat k)dot

Find the vector equation of the plane passing through three points with position vectors hat i+ hat j-2hatk, 2hat i-\ hat j+ hat k and hat i+2 hat j+ hat kdot Also find the coordinates of the point of intersection of this plane and the line vec r=3 hat i-\ hat j- hat k+lambda(2 hat i-\ 2 hat j+ hat k)dot