00:01
Here in this portion we are given the two lines l1 equals to x minus 3 divided by 2 equals to y plus 1 divided by 4 equals to z minus 2 divided by minus 1 similarly l2 equals to x minus 1 by 4 equals to y minus 1 upon 2 equals to z plus 3 upon 4 now here first of we need to check whether this l1 and i2 intersect each other.
00:37
Here we will make the equation of l1 in terms of t and equation of l2 in terms of as as x equals to 2 t plus 3 similarly y equals to 4t minus 1 and z equals to minus 2 plus 2 now for this l2 we have x equals to 4 s plus 1 y equals to 2 s plus 1 and z equals to 4 s minus 3 now we are using this equation we have 2 t plus 3 equals to 4 s plus 1 therefore unsuplifying this we have 2 t plus 2 2 equals to 4 s and for 5 coordinate we have 40 minus 1 equals to 2 s plus 1.
01:36
Therefore i'm simplifying this.
01:38
Here we have 40 minus 2 s equals to 2.
01:46
Now here using this equation 1 and 2 we can obtain the value of s equals to 1 and d therefore here further we have minus t plus 2 which can be written as minus 1 plus 2 equals to 1 and similarly for 4 s minus 3 we have 4 minus 3 which is equal to 1 therefore both this value are equal which can be written as minus 2 equals to 4 s minus 3 here hence we have concluded that l 1 and 2 is l to intersect each other.
02:45
Now here further, let us assume that coordinates of intersection will be by substituting the value of t and s in the above equations.
03:05
Here we have coordinate as x, y, z equals to 5 .3, comma, 1.
03:14
Now here our next strategy we need to find the value of cosine of intersection of this line.
03:23
Therefore here to find cosine of intersection we will consider the direction factors of line.
03:45
For the line l1 we have v1 equals to 2 .4 .5 minus...