[" The length of the perpendicular drawn...

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

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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:

vec r=(4hat i-hat j)+lambda(hat i+2hat j-3hat k) and vec r=(hat i-hat j+2hat k)+mu(2hat i+4hat j-5hat k)

Equation of the plane containing the lines vec r=(hat i-2hat j+hat k)+t(hat i+2hat j-hat k)vec r=(hat i+2hat j-hat k)+s(hat i+hat j+3hat k) is

Shortest distance between the lines: vec r=(4hat i-hat j)+lambda(hat i+2hat j-3hat k) and vec r=(hat i-hat j+2hat k)+u(2hat i+4hat j-5hat k)

Find the shortest distance between the lines vec r=(4hat i-hat j)+lambda(hat i+2hat j-3hat k) and vec r=(hat i-hat j+2hat k)+mu(2hat i+4hat j-5hat k)

Consider a line vec r=hat i+t(hat i+hat j+hat k) and a plane (vec r-(hat i+hat j))*(hat i-hat j-hat k)=1

Equation of the plane that contains the lines r=(hat(i)+hat(j))+lambda(hat(i)+2hat(j)-hat(k)) and , r=(hat(i)+hat(j))+mu(-hat(i)+hat(j)-2hat(k)) is

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

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