Show that the points `A(6,-7,0),B(16 ,-19 ,-4),C(0,3,-6)a n d` `D(2,-5,10)` are such that `A B` and `C D` intersect at the point `P(1,-1,2)dot`

Explanation

` vec{A P} =(hat{i}-hat{j}+2 hat{k})-(6 hat{i}-2 hat{j}+0 hat{k}) =-5 hat{i}+6 hat{j}+2 hat{k}`

`vec{P B}=(16 hat{i}-19 hat{j}-4 hat{k})-(hat{i}-hat{j}+2 hat{k})`

`=15 hat{i}-18 hat{j}-6 hat{k}`.

`=-3(-5 hat{i}+6 hat{j}+2 hat{k})`

`vec{P B}=-3(vec{A P}) `

`A, P B` are collinear.

`vec{C P}=(hat{i}-hat{j}+2 hat{k})-(0 hat{i}+3 hat{j}-6 hat{k})`

`=hat{i}-4 hat{j}+8 hat{k}`

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