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 length and the foot of the perpendicular from the point (1,1,2) to the plane vec a*(hat i2hat j+4hat k)+5=0

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 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), wher lambda is a parameter.

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.

Write the plane vec rdot((2 hat i+3 hat j-6 hat k)=14 in normal form.

Write the vector equation of the line passing through the point (1, -2, -3) and normal to the plane vec rdot((2 hat i+ hat j+2 hat k)=5.

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 vector equation of the line through the origin which is perpendicular to the plane vec rdot(( hat i+2 hat j+3 hat k)=3.

Find the distance of the point 2hat i+hat j-hat k from the plane vec r*(hat i-2hat j+4hat k)=9

Find the distance of the point 2 hat i- hat j-4 hat k from the plane vec rdot((3 hat i-4 hat j+12 hat k)-9=0.