1. Find a parametric equations of the line containing the point $$ A $$ and parallel to the vector $$ v $$. a) $$ A(-2,1,3), v=2 i+6 j-5 k $$ b) $$ A(4,-2,3), v=3 i+6 j-2 k $$ c) $$ A(2,-3,7), v=4 i+6 j-12 k $$

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**a)** Given $$ A(-2,1,3) $$ and $$ v = 2i + 6j - 5k $$, the line through $$ A $$ with direction $$ v = (2,6,-5) $$ has parametric equations:  
$$
x = -2 + 2t,
$$
$$
y = 1 + 6t,
$$
$$
z = 3 - 5t.
$$

**b)** Given $$ A(4,-2,3) $$ and $$ v = 3i + 6j - 2k $$, the line through $$ A $$ with direction $$ v = (3,6,-2) $$ has parametric equations:  
$$
x = 4 + 3t,
$$
$$
y = -2 + 6t,
$$
$$
z = 3 - 2t.
$$

**c)** Given $$ A(2,-3,7) $$ and $$ v = 4i + 6j - 12k $$, the line through $$ A $$ with direction $$ v = (4,6,-12) $$ has parametric equations:  
$$
x = 2 + 4t,
$$
$$
y = -3 + 6t,
$$
$$
z = 7 - 12t.
$$
**a)** The parametric equations for the line through $$ A(-2,1,3) $$ with direction $$ v = (2,6,-5) $$ are: $$ x = -2 + 2t, $$ $$ y = 1 + 6t, $$ $$ z = 3 - 5t. $$ **b)** The parametric equations for the line through $$ A(4,-2,3) $$ with direction $$ v = (3,6,-2) $$ are: $$ x = 4 + 3t, $$ $$ y = -2 + 6t, $$ $$ z = 3 - 2t. $$ **c)** The parametric equations for the line through $$ A(2,-3,7) $$ with direction $$ v = (4,6,-12) $$ are: $$ x = 2 + 4t, $$ $$ y = -3 + 6t, $$ $$ z = 7 - 12t. $$

Find a parametric equations of the line containing the point and parallel to the vector .
a)
b)
c)

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