### Video Transcript

Give the Cartesian equation of the
line π« equals negative three, negative two, negative two plus π‘ four, two,
four.

In this question, weβre given this
equation in vector form. Negative three, negative two,
negative two is the position vector of a given point, and four, two, four is the
direction vector. In order to change the equation in
vector form into an equation in Cartesian form, there is a formula we can apply. The equation of a line with
direction vector π― equals π, π, π that passes through π₯ sub one, π¦ sub one, π§
sub one is given by π₯ minus π₯ sub one over π equals π¦ minus π¦ sub one over π
equals π§ minus π§ sub one over π, where π, π, and π are nonzero real
numbers.

We now need to take the direction
vector four, two, four to have the values of π, π, and π, respectively. We can do the same and designate
the coordinate π₯ sub one, π¦ sub one, π§ sub one with the values negative three,
negative two, negative two. Plugging these values into the
formula, we have π₯ minus negative three over four equals π¦ minus negative two over
two equals π§ minus negative two over four. Simplifying the numerators, we have
π₯ plus three over four equals π¦ plus two over two equals π§ plus two over
four. And thatβs the answer for the
Cartesian equation of the given line.