Question

Find a vector equation and parametric equations for the line through the point (7,4, 5) and parallel to the vector 3i 2j-k .

Answer 1

Answer: vector equation r = (7+3t)i + (4+2t)j + (5 - 5t)k

parametric equations: x = 7 + 3t; y = 4 + 2t; z = 5 - 5t

Step-by-step explanation: The vector equation is a line of the form:

r = $r_{0}$ + t.v

where

$r_{0}$ is the position vector;

v is the vector;

For point (7,4,5):

$r_{0}$ = 7i + 4j + 5k

Then, the equation is:

r = 7i + 4j + 5k + t(3i + 2j - k)

r = (7 + 3t)i + (4 + 2t)j + (5 - 5t)k

The parametric equations of the line are of the form:

x = $x_{0}$ + at

y = $y_{0}$ + bt

z = $z_{0}$ + ct

So, the parametric equations are:

x = 7 + 3t

y = 4 + 2t

z = 5 - 5t