Question

6.Find the cartesian equation of the line which passes through the point (-2,4,-5)and parallel to the line given byTlel to the line given by3y-4.z+8

Answer 1

It is given that the line passes through the point ( −2,4,−5 ) and is parallel to the line x+3 3 = y−4 5 = z+8 6 . Consider that the line is passing through a point ( x ′ , y ′ , z ′ )and parallel to the line with direction ratios a,b,c which is given as,

x− x ′ a = y− y ′ b = z− z ′ c (1)

The line is parallel to x+3 3 = y−4 5 = z+8 6 .

So, compare the above line equation with equation (1). Then the values of direction ratios are,

a=3k b=5k c=6k

Compare the position vector ( x ′ , y ′ , z ′ )with ( −2,4,−5 )in equation (1).

x ′ =−2 y ′ =4 z ′ =−5

Equation of the line in Cartesian form becomes,

x−( −2 ) 3k = y−4 5k = z−( −5 ) 6k x+2 3 = y−4 5 = z+5 6 =k

Thus, the equation of the line is x+2 3 = y−4 5 = z+5 6 =k.