Find the equation of the line joining the points?

Question

Find the equation of the line joining the points

(7, 9, ─3) and (11, ─5, ─2).

Answer 1

Given the two points P(7, 9, -3) and Q(11, -5, -2), write the equation of the line joining the two points.

Define the directional vector of the line v.

v = PQ = <7, 9, -3> - <11, -5, -2> = <-4, 14, -1>

Any non-zero multiple of the directional vector is still a directional vector. Multiply by -1.

v = <4, -14, 1>

With the directional vector and one of the points we can write the equation of the line L.

L = P + tv
L = <7, 9, -3> + t<4, -14, 1>
where t is a scalar ranging over the real numbers

Answer 2

section a) making use of distance formulation :- d² = (6 - 3)² + (11 - 7)² d² = 9 + sixteen d² = 25 d = 5 section b) m = (11 - 7) / (6 - 3) m = 4 / 3 y - b = m (x - a) :- y - 7 = (4/3) (x - 3) y = (4/3) x - 4 + 7 y = (4/3) x + 3

Answer 3

x-7/7-11 = y-9/9--5=z--3/-3--2
x-7/-4 = y-9/14 = z+3/-1
(7-x)/4 = (y-9)/14 = -(z+3)