The vector form and parametric forms of a line, given a point and direction, or given two points

For each of the following lines, write its equation in vector form and parametric form:

a) The line passes through the point $P_0 (1, 2, 4)$ in the direction of $v= [5, -3, 1]$.

Vector equation:

$[x, y, z] = [1,2,4] + t[5,-3,1]$

Parametric form:

$x = 1 + 5t, y = 2 - 3t, z = 4 + t$

b) The line passes through points $P_0( -3, 5, 8)$ and $P_1(4, 2, -1)$.

Solution:

v = $P_1 - P_0 = [7, -3, -9]$

Vector form:

$[x, y, z] = [ -3, 5, 8] + t[7, -3, -9]$

Parametric form:

$x = -3 + 7t, y = 5 - 3t, z = 8 -9t$

right?

1 Answer

Right ! Everything is fine, well done.