1. Example-1
1. Find isCollinear(A,B)
`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.
2. Find isCollinear(A,B)
`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)=0.5`
`(A_2)/(B_2)=(4)/(8)=0.5`
Since `(A_1)/(B_1)=(A_2)/(B_2)`, So vectors are collinear.
3. Find isCollinear(A,B)
`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=0.6667`
`0.6667 * vec A`
`=(0.6667*A_1,0.6667*A_2,0.6667*A_3)`
`=(0.6667*3,0.6667*4,0.6667*0)`
`=(2,2.6667,0)`
`!=vec B`
Since `vec B != 0.6667 * vec A`, so vectors are not collinear.
This material is intended as a summary. Use your textbook for detail explanation.
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