Using vectors show that the points `A(-2,3,5),B(7,0,-1)C(-3,-2,-5)` and `D(3,4,7)` are such that `A B` and `C D` intersect at the point `P(1,2,3)dot`

Explanation

We are given points


`A(-2,3,5) quad B(7,0,1) quad C(-3,-2,-5) quad D(3,4,7)`


Line passing through the points `A` and `B` is


`vec(A)+t(vec(B)-vec(A))=-2 hat i+3 hat j+5 hat k+t((7-(-2)) hat i+(0-3) hat j+(1-5) hat k)`


`=-2 hat i+3 hat j+5 hat k+ t(9 hat i-3 hat j-4 hat k)`


`rArr (9t-2) hat i+(3-3t) hat j+(5-4t) hat k quad ---(1)`


And line passing through point `C` and `D` is


`vec C+s(vec D- vec C)=-3 hat i-2 hat j-5 hat k +s((3-(-3)) hat i+(4-(-2)) hat j+(7-(-5)) hat k)`


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