Equations for a Line Passing Through a Point with Given Direction Angles

[f22archrer]

Homework Statement

A line has direction angles 60°, 45°, 60° and passes through the point (1, -2, 5). Determine vector, parametric and symmetric equations of this line.

Homework Equations

The Attempt at a Solution

1/2 i + [root 2]/2 j +1 /2 k
parametric equation will be [1 ,-2, 5]
x= 1/2t+1
y=[root 2] /2 t+2
z=1/2 t+5

[x,y]= [1,2] + t[1/2,root2/2]

symmetrical
[x-1]/.5= {y-2]/[root2/2]}=[z-5]/.5

thats my final answer... please check if i have done it the proper way...

 

[BruceW]

x= 1/2t+1
y=[root 2] /2 t+2
z=1/2 t+5

Hey archer. I hope this reply is not too late for you. Anyway, you are very close to the parametric equation of the line. Remember the line passes through the point (1,-2,5) So your equation has one slight mistake in it.

[x,y]= [1,2] + t[1/2,root2/2]

symmetrical
[x-1]/.5= {y-2]/[root2/2]}=[z-5]/.5

Again, you are really close, the x and z parts are correct, but you have made the same slight mistake with the y part.

1/2 i + [root 2]/2 j +1 /2 k

This is part of the answer for the vector equation of the line, but there is more. hint: will this vector equation take you from the origin to any general point on the line?

 

[f22archrer]

thanks