[" A line passes through "(2,-1,3)" and is perpendicular to "],[" the lines "r*(hat i+hat j-hat k)+lambda(2hat i-2hat j+hat k)" and "],[r=(2hat i-hat j-3hat k)+mu(hat i+2hat j+2hat k)" obtain its equation."]

A line passes through (2, -1, 3) and is perpendicular to the line -> r=( hat i+ hat j- hat k)+lambda(2 hat i-2 hat j+ hat k)a n d\ -> r=(2 hat i- hat j-3 hat k)+mu( hat i+2 hat j+2 hat k)dot obtaining its equation.

A line passes through (1, -1, 3) and is perpendicular to the lines r*(hat(i)+hat(j)-hat(k))+lambda(2hat(i)-2hat(j)+hat(k)) and r=(2hat(i)-hat(j)-3hat(k))+mu(hat(i)+2hat(j)+2hat(k)) obtain its equation.

A line passes through (1, -1, 3) and is perpendicular to the lines r*(hat(i)+hat(j)-hat(k))+lambda(2hat(i)-2hat(j)+hat(k)) and r=(2hat(i)-hat(j)-3hat(k))+mu(hat(i)+2hat(j)+2hat(k)) obtain its equation.

A line passes through (1, -1, 3) and is perpendicular to the lines vecr=(hat(i)+hat(j)-hat(k))+lambda(2hat(i)-2hat(j)+hat(k)) and vecr=(2hat(i)-hat(j)-3hat(k))+mu(hat(i)+2hat(j)+2hat(k)). Obtain its equation.

A line passes through (1, -1, 3) and is perpendicular to the lines vecr=(hat(i)+hat(j)-hat(k))+lambda(2hat(i)-2hat(j)+hat(k)) and vecr=(2hat(i)-hat(j)-3hat(k))+mu(hat(i)+2hat(j)+2hat(k)). Obtain its equation.

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)

A line passes through (2,-1,3) and perpendicular to the lines vec(r)=(hat(i)+hat(j)+hat(k))+lamda(2hat(i)-2hat(j)+hat(k)) and vec(r)=(2hat(i)-hat(j)-3hat(k))+mu(hat(i)+2hat(j)+2hat(k)) . Obtain its vector equation.

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

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

If vec r=(hat i+2hat j+3hat k)+lambda(hat i-hat j+hat k) and vec r=(hat i+2hat j+3hat k)+mu(hat i+hat j-hat k) are bisector of two lines is