1. Find Collinear vectors
`A=(3,4,5)`, `B=(6,8,10)`

Solution:
Here `vec A=(3,4,5),vec B=(6,8,10)`

Two vectors are collinear if relations of their coordinates are equal.
`(A_1)/(B_1)=(3)/(6)=1/2`

`(A_2)/(B_2)=(4)/(8)=1/2`

`(A_3)/(B_3)=(5)/(10)=1/2`

Since `(A_1)/(B_1)=(A_2)/(B_2)=(A_3)/(B_3)`, So vectors are collinear.

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2. Find Collinear vectors
`A=(3,4)`, `B=(6,8)`

Solution:
Here `vec A=(3,4),vec B=(6,8)`

Two vectors are collinear if relations of their coordinates are equal.
`(A_1)/(B_1)=(3)/(6)=1/2`

`(A_2)/(B_2)=(4)/(8)=1/2`

Since `(A_1)/(B_1)=(A_2)/(B_2)`, So vectors are collinear.

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3. Find Collinear vectors
`A=(3,4,0)`, `B=(2,2,1)`

Solution:
Here `vec A=(3,4,0),vec B=(2,2,1)`

Two vectors `vec A` and `vec B` are collinear if there exists a number n such that `vec B = n * vec A`

Find the first nonzero coefficient of vector `vec A`

`A_1=3`

`n=B_1/A_1=2/3=2/3`

`2/3 * vec A`

`=(2/3*A_1,2/3*A_2,2/3*A_3)`

`=(2/3*3,2/3*4,2/3*0)`

`=(2,8/3,0)`

`!=vec B`

Since `vec B != 2/3 * vec A`, so vectors are not collinear.

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