Find the shortest distance between the lines r = (1, 5, 6) + y(-2, -1, 0) and r = (1, 7, -3) + z(2, 0, 4)

Vector joining the two lines = (1, 5, 6) - (1, 7, -3) = (0, -2, 9)Normal vector to the two lines = (-2, -1, 0) x (2, 0, 4) = (-4, 8, 2) = 2(-2, 4, 1)Hence, using the dot product, shortest distance = (0, -2, 9) "dot" (-2, 4, 1) / sqrt(22 + 42 + 12) = -8 + 9 / sqrt(4 + 16 + 1) = 1/sqrt(21)

AH
Answered by Abhinav H. Further Mathematics tutor

1975 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

How does proof by mathematical induction work?


A child weighing 50kg is pushed down a 2m long slide (u=0.1), angled at 45 degrees from the horizontal, at 5m/s. At what speed does the child reach the bottom of the slide?


Given that f(x)=2sinhx+3coshx, solve the equation f(x)=5 giving your answers exactly.


Take quadratic equation x^2-6x+14=0 and its solutions a and b. What is a/b+b/a?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences