Question

(a) Find the parametric equation of the straight line with non-parametric equation 2x ? y = 3.

(b) Find the parametric equation of L1 if L1 is a straight line in 3D passing through the points (1, 2, 3) and (4, 4, ?2). (c) Show that L1 also passes through the point (?5, ?2, 13).

Answer 1

Answer :

a) Consider the non parametric equation

2x -y = 3

Set x = t then y = 2t - 3 where t is a parameter.

So the parametric equation of the straight line is

x=t , y = 2t-3

b) The parametric equation of the line L1 passing through the given points is

( x, y, z ) = (1,2,3)+t((4,4,-2)-(1,2,3))

= ( 1,2 3 ) + t( 3, 2, -5)

= ( 1+3t , 2+2t , 3-5t)

The parametric equations of the line L1 are

x = 1 + 3t , y = 2 + 2t , z = 3 - 5t

c) substituting t = -2 in the above parametric equations, we get

x = 1 +3(-2) = 1-6 = -5

y = 2 + 2(-2) = 2 - 4 = - 2

and z = 3 - 5(-2) = 3 + 10 = 13

Hence. the line L1 is passing through the point ( - 5 , - 2 , 13 )