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

3296 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

Finding modulus and argument of complex number (x+iy)

When using the method of partial fractions how do you choose what type of numerator to use and how do you know how many partial fractions there are?

Prove by mathematical induction that 2^(2n-1) + 3^(2n-1) is divisible by 5 for all natural numbers n.

FP3- Find the eigenvalues and the eigenvector for the negative eigenvalue, from this 2x2 matrix of columns (2,1) and (3,0)