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

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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.

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

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

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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

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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

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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?