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

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 = + t.v

where

is the position vector;

v is the vector;

For point (7,4,5):

= 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 = + at

y = + bt

z = + ct

So, the parametric equations are:

x = 7 + 3t

y = 4 + 2t

z = 5 - 5t

x=-7

step-by-step explanation:

x+3=-10

-10+3=-7

x=-7