Home
Class 12
MATHS
A line passes through (1, -1, 3) and is ...

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.

Text Solution

Verified by Experts

The correct Answer is:
`r=(hat(i)-hat(j)+3hat(k))+mu(2hat(i)+hat(j)-2hat(k))`
Promotional Banner

Similar Questions

Explore conceptually related problems

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

Find the angle between the pair of lines r=3hat(i)+2hat(j)-4hat(k)+lambda(hat(i)+2hat(j)+2hat(k)) r=5hat(i)-4hat(k)+mu(3hat(i)+2hat(j)+6hat(k))

Find the angle between the pairs of line r=3hat(i)+2hat(j)-4hat(k)+lambda(hat(i)+2hat(j)+2hat(k)) and hat(r)=5hat(i)-2hat(j)+mu(3hat(i)+2hat(j)+6hat(k)) .

Find a unit vector perpendicular to both the vectors (2hat(i)+3hat(j)+hat(k)) and (hat(i)-hat(j)-2hat(k)) .

The distance between the line r=2hat(i)-2hat(j)+3hat(k)+lambda(hat(i)-hat(j)+4hat(k)) and the plane rcdot(hat(i)+5hat(j)+hat(k))=5, is

Find the shortest distance and the vector equation of the line of shortest distance between the lines given by r=(3hat(i)+8hat(j)+3hat(k))+lambda(3hat(i)-hat(j)+hat(k)) and r=(-3hat(i)-7hat(j)+6hat(k))+mu(-3hat(i)+2hat(j)+4hat(k)) .

Find the unit vector perpendicular the plane rcdot(2hat(i)+hat(j)+2hat(k))=5 .

The line whose vector equation are r=2hat(i)-3hat(j)+7hat(k)+lambda(2hat(i)+phat(j)+5hat(k)) and r=hat(i)+2hat(j)+3hat(k)+mu(3hat(i)-phat(j)+phat(k)) are perpendicular for all values of lambda and mu if p eqauls to

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

Find the shortest distance between the lines vec r=(4 hat i- hat j)+lambda( hat i+2 hat j-3 hat k)a n d vec r=( hat i- hat j+2 hat k)+mu(2 hat i+4 hat j-5 hat k)dot .