Answers>Further Mathematics>A Level>Article

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)

Answered by Abhinav H. • Further Mathematics tutor

3015 Views

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

Related Further Mathematics A Level answers

Using a Suitable substitution or otherwise, find the differential of y= arctan(sinxcosx), in terms of y and x.

Find, without using a calculator, integral of 1/sqrt(15+2x-x^2) dx, between 3 and 5, giving your answer as a multiple of pi

Differentiate arcsin(2x) using the fact that 2x=sin(y)

Using z=cos(θ)+isin(θ), find expressions for z^n-1/z^n and z^n+1/z^n