Home
Class 12
MATHS
Find the angle between the pair of lines...

Find the angle between the pair of lines
`vec(r)=3hat(i)+5hat(j)-hat(k)+lambda(hat(i)+hat(j)+hat(k))" and "vec(r)=7hat(i)+4hat(k)+mu(2hat(i)+2hat(j)+2hat(k))`

Text Solution

Verified by Experts

The correct Answer is:
`0^(@)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    OSWAAL PUBLICATION|Exercise Topic -2 (Short answer type questions-I)|6 Videos

  • THREE DIMENSIONAL GEOMETRY

    OSWAAL PUBLICATION|Exercise Topic -2 (Short answer type questions-II)|23 Videos

  • THREE DIMENSIONAL GEOMETRY

    OSWAAL PUBLICATION|Exercise Topic - 3 (Long answer type questions - II)|23 Videos

  • SOLVED PAPER ( Topper Answers March - 2015 )

    OSWAAL PUBLICATION|Exercise PART - E|4 Videos

  • VECTOR ALGEBRA

    OSWAAL PUBLICATION|Exercise Topic - 4 (Short Answer Type Questions - II|7 Videos

Similar Questions

Explore conceptually related problems

Find the angle between the following pairs of lines : r=2hat(i)-5hat(j)+hat(k)+lambda(3hat(i)+2hat(j)+6hat(k)) " and " r=7hat(i)-6hat(k)+mu(hat(i)+2hat(j)+2hat(k))

Find the angle between the following pairs of lines : vec(r)=3hat(i)+2hat(j)-4hat(k)+lambda(hat(i)+2hat(j)+2hat(k)) " & " vec(r)=5hat(i)-2hat(j)+mu(3hat(i)+2hat(j)+6hat(k)) Note : Angle between two lines is the angle between vec(b_(1)) " and " vec(b_(2))

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 following pairs of lines : r=3hat(i)+hat(j)-2hat(k)+lambda(hat(i)-hat(j)-2hat(k)) " and " r=2hat(i)-hat(j)-56hat(k)+mu(3hat(i)-5hat(j)-4hat(k)) .

Find the distance between the parallel lines vec(r)=hat(i)+2hat(j)-4hat(k)+m(2hat(i)+3hat(j)+6hat(k)) " and " vec(r)=3hat(i)+3hat(j)-5hat(k)+n(2hat(i)+3hat(j)+6hat(k))

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

Find the vector equation of the plane that contains the lines vec(r) = (hat(i) + hat(j)) = lambda (hat(i) + 2 hat(j) - hat(k)) and vec(r) =(hat(i) + hat(j)) + mu (- hat(i) + hat(j) - 2 hat(k)) . Also find the length of perpendicular drawn from the point (2,1,4) to the plane thus obtained .

Find the angle between the vectors vec(a) = hat(i) + hat(j) + hat(k) and vec(b) = hat(i) - hat(j) + hat(k) .

Find the vector and cartesian equations of a plane containing the two lines vec(r) = (2 hat(i) + hat(j) - 3 hat(k)) + lambda(hat(i) + 2 hat(j) + 5 hat(k)) and vec(r) = (3hat(i) + 3 hat(j) + 2 hat(k)) + lambda (3 hat(i) - 2 hat(j) + 5 hat(k)) . Also show that the line vec(r) = (2 hat(i) + 5 hat(j) + 2 hat(k)) + p (3 hat(i) - 2 hat(j) + 5 hat(k)) lies in the plane.

By computing the shortest distance between the following pair of lines, determine whether they intersect or not. vec(r) = (hat(i) - hat(j) ) + lambda (2 hat(i) -hat(k)) and vec(r) = (2 hat(i) - hat(j)) + mu (hat(i) - hat(j) - hat(k)) .

Home
Profile