00:01
In this question, we are asked to find the parametric equations and symmetric equation.
00:14
So we are given two points, point a, 2 comma 4 comma negative 3 and point b as 3 comma negative 1 comma 1.
00:28
So first let's find the vector v that is parallel to the line, let's say ab vector, which is going to be b subtracted by a coordinate and next we will be having negative 1 subtracted by negative 4 and 1 plus 3.
00:47
So this is going to be 1 comma negative 5 comma 4.
00:53
So the directions, this is going to be small a, b and c.
00:59
So let's take the point 2 comma 4 comma negative 3 to find the parametric equation.
01:06
So let's say, so consider point 2 comma 4 comma negative 3.
01:16
So from this week, we are going to construct the parametric equation.
01:19
So let's take x is equals to the first coordinate and first coordinate combined with a variable t.
01:27
So here it is going to be 4 subtracted by 5t and negative 3 subtracted by 4t.
01:35
Sorry, this is plus and here it is negative 5t.
01:39
So this is x and this is y and this is z.
01:44
These are the parametric equations.
01:47
So this is the general form.
01:49
So parametric equation on the whole, i'll write it as x is equals to 2 plus t, y is equals to 4 negative 5t, z is equals to 4t subtracted by 3.
02:05
So this is the required parametric equation.
02:08
So moving on to symmetric equation, let's consider it's given that symmetric equation is going to be of the form x subtracted by the point 2 over this a.
02:29
So which is going to be 1 and we'll be having y subtracted by y...