The point of intersection of the lines x-53=y-7-1=z+21 and x+3-36=y-32=z-64 is - Maths -

Question

The point of intersection of the lines
x - 5 3 = y - 7 - 1 = z + 2 1   and   x + 3 - 36 = y - 3
2 = z - 6 4 is

Lovina Kansal · Accepted Answer

Dear student
We have,x-53=y-7-1=z+21=λ   (say)     
(1)x+3-36=y-32=z-64=k   (say)      
(2)Let P(3λ+5,-λ+7,λ-2) be any point on the line (1)Let Q-36k-3,2k+3,4k+6 be any point on the line (2)If the lines (1) and (2) intersect,the P and Q must coincide for some particular values of λ and k
This gives,3λ+5=-36k-3    
(3)-λ+7=2k+3        
(4)λ-2=4k+6⇒λ-4k=8            
(5)Solving (3) and (4), we getλ=163 and k=-23Putting λ=163 and k=-23 in LHS of (5), we getLHS=163+83=8=RHSHence, the given lines intersect
Now, we will put λ=163 and k=-23 in either P or Q to get point of intersection
So, the coordinates of point of intersection of line (1) and line (2) are P21,53,103 Or Q 21,53,103
Regards

The point of intersection of the lines x - 5 3 = y - 7 - 1 = z + 2 1 and x + 3 - 36 = y - 3 2 = z - 6 4 is

The point of intersection of the lines
$\frac{x - 5}{3} = \frac{y - 7}{- 1} = \frac{z + 2}{1} and \frac{x + 3}{- 36} = \frac{y - 3}{2} = \frac{z - 6}{4}$ is