[tex]\text{We have been given that}\\ r(t)=<-4-2t,20+6t,26+8t>\\ r(s)=<-13+7s,15-5s,4+s>\\ \text{In order to find the intersection point, the x, y and z } \\ \text{coordinates should be same}\\ \text{Thus, we have}\\ -4-2t=-13+7s\\ 7s+2t=9\\ 2t=9-7s\\ t=\frac{1}{2}(9-7s)............(1)\\ \\ 20+6t=15-5s\\ 5s+6t=-5............(2)\\ \text{On solving equation 1 and 2} 5s+6\cdot \frac{1}{2}(9-7s)= -5\\ \\ 27-16s=-5\\ 16s= 32\\ s=2\\[/tex]
[tex]\text{Thus, the value for t is }\\ t=\frac{1}{2}(9-7\cdot 2)\\ \\ t=-\frac{5}{2}\\ \\ \text{Thus, the intersection point is given by}\\ \left (-4-2\cdot -\frac{5}{2},20+6\cdot -\frac{5}{2},26+8\cdot -\frac{5}{2} \right )\\ \\ =(1,5,6)[/tex]
The intersection point is given by (1,5,6)
