# vectors.lines.planes

• Dec 1st 2007, 01:56 PM
xfyz
vectors.lines.planes
1) Find a vector equation and parametric equations for the line through the origin and parallel to the line x=2t, y=1-t, z=4+3t.

2) Find parametric and symmetric equations for the line through (2,1,0) and perpindicular to both i+j and j+k

can someone help me with these? thanks
• Dec 1st 2007, 04:34 PM
Jhevon
Quote:

Originally Posted by xfyz
1) Find a vector equation and parametric equations for the line through the origin and parallel to the line x=2t, y=1-t, z=4+3t.

Hint: you want the line passing through (0,0,0) with direction vector <2,-1,3>

Quote:

2) Find parametric and symmetric equations for the line through (2,1,0) and perpindicular to both i+j and j+k
Hint: you want the line passing through (2,1,0) with direction vector given by <1,1,0> X <0,1,1>, where X means the cross-product
• Dec 2nd 2007, 07:46 PM
xfyz
Quote:

Originally Posted by Jhevon
Hint: you want the line passing through (0,0,0) with direction vector <2,-1,3>

Hint: you want the line passing through (2,1,0) with direction vector given by <1,1,0> X <0,1,1>, where X means the cross-product

1.
r = ro + tv

t(2i-j+3k) the vector eq
x = 2t, y = -t, z = 3t the parametric

2.
r = ro+tv after cross product

v = <1,-1,1>

r = (2i+j) + t(i-j+k)

r = i(2+t)+j(1-t)+k(t) the vector eq

x = 2+t , y = 1-t , z = 1 the parametric

is this right?