show that the points whose position vectors are `(-2hat(i) +3hat(j) +5hat(k))`
`(hat(i)+2hat(j)+3hat(k)) " and " (7hat(i) -hat(k))` are collinear.

Explanation

the coordinates of the given points are A(-2,3,5) B(1,2,3) and C(7,0,-1)
The equation of line AB are
`(x+2)/(1+2) =(y-3)/(2-3) =(z-5)/(3-5)rArr (x+2)/(3)=(y-3)/(-1) =(z-5)/(-2)`
Putting x=7 , y=0 and z=-1 in (i) we get
`(7+2)/(3)+(0-3)/(-1) =(-1 -5)/(-2)` which is clearly true .
Thus the point C(7,0,-1) satisfies the equation of line AB
`:. ` C lies on line AB
Hence the given points A, B and C are collinear.