Question

Given that A = (9,9,2), B = (1,3,5) and C = (5,6,4), find the vector equation of the line through A and B

Answer 1

Equation = 9i + 9j + 2k - λ ( 8i + 6j - 3k)

Explanation:

Vector equation of a line passing through two points A & B is : r = a + λ(b - a)

Given A = (9,9,2) ; B = (1,3,5)

Equation of line : r = 9i + 9j + 2k + λ [ (1-9) i + (3-9) j + (5-2) k ]

= 9i + 9j + 2k + λ ( -8i + -6j + 3k)

= 9i + 9j + 2k - λ ( 8i + 6j - 3k)