A line has Cartesian equations given by

Question

x-1/3=y+2/4=z-4/5

a) Give the coordinates of the point on the line
b) Give the vector parallel to the line
c) Write down the equation of the line in parametric form
d) Determine the Cartesian equation of the plane that is perpendicular to the line and passes through the point (2,3,-1)

Answer 1

I am sure you meant:
(x-1)/3 = (y+2)/4 = (z-4)/5

a) Give the coordinates of the point on the line
this is a poorly worded question, since we have an infinite number of points on this line
one of them is (1,-2,4)

b) you MUST know how to find the answer to this!!!

c) find the cross product with <3, 4, 5> as your first step.

(check my taking the dot product of your answer with <3, 4, 5> , it must be zero.
After that, just write down the equation, you have a point and the direction numbers.

Answer 2

a line has cartesian equation x-1/3