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

Topper's Solved these Questions

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|44 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|26 Videos

  • THEORY OF EQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|35 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

Similar Questions

Explore conceptually related problems

The equation of line passing through (3,-1,2) 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)) is

Find the equations of a line passing through the point P(2,-1,3) and perpendicular to the lines vec(r ) =(hat(i) + hat(j) -hat(k)) +lambda (2hat(i) -2hat(j) +hat(k)) and vec( r) =(2hat(i) -hat(j) -3hat(k)) +mu (hat(i) +2hat(j) +2hat(k))

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.

Find the equation in vector and cartesian form of the line passing through the point : (2,-1, 3) and perpendicular to the lines : vec(r) = (hat(i) + hat(j) - hat(k)) + lambda (2 hat(i) - 2 hat(j) + hat(k)) and vec(r) = (2 hat(i) - hat(j) - 3 hat(k) ) + mu (hat(i) + 2 hat(j) + 2 hat(k)) .

(A ) Find the vector and cartesian equations of the line through the point (5,2,-4) and which is parallel to the vector 3 hat(i) + 2 hat(j) - 8 hat(k) . (b) Find the equation of a line passing through the point P(2, -1, 3) and perpendicular to the lines : vec(r) = (hat(i) + hat(j) - hat(k) ) + lambda (2 hat(i) - 2 hat(j) + hat(k)) and vec(r) = (2 hat(i) - hat(j) - 3 hat(k) ) + mu (hat(i) + 2 hat(j) + 2 hat(k)) .

Show that the lines vec(r) =(hat(i) +2hat(j) +hat(k)) +lambda (hat(i)-hat(j)+hat(k)) " and " vec(r ) =(hat(i) +hat(j) -hat(k)) + mu (hat(i)- hat(j) + 2hat(k)) Do not intersect .

vec(r )=(-4hat(i)+4hat(j) +hat(k)) + lambda (hat(i) +hat(j) -hat(k)) vec(r)=(-3hat(i) -8hat(j) -3hat(k)) + mu (2hat(i) +3hat(j) +3hat(k))

The angle between the line r=(hat(i)+2hat(j)-hat(k))+lamda(hat(i)-hat(j)+hat(k)) and the plane r*(2hat(i)-hat(j)+hat(k))=4 is