PG1995
Active Member
Hi
[laTEX]$Two\hspace{0.06in}vectors\hspace{0.06in}\overrightarrow{a}\hspace{0.06in}and\hspace{0.06in}\overrightarrow{b}\hspace{0.06in}are\hspace{0.06in}parallel\hspace{0.06in}if\hspace{0.06in}\frac{a_{1}}{b_{1}}=\frac{a_{2}}{b_{2}}=\frac{a_{3}}{b_{3}}=\lambda ,\hspace{0.06in}[/laTEX][laTEX]where\hspace{0.06in}\overrightarrow{a}=a_{1}i+a_{2}j+a_{3}k\hspace{0.06in}\overrightarrow{b}=b_{1}i+b_{2}j+b_{3}k$[/laTEX]
But I have been told that we also get the same result even when the two vectors are collinear. Then, how do we know that if they are parallel or collinear? Two parallel straight lines have different y-axis intercepts if they are not collinear. What do you say? Thank you.
Regards
PG
[laTEX]$Two\hspace{0.06in}vectors\hspace{0.06in}\overrightarrow{a}\hspace{0.06in}and\hspace{0.06in}\overrightarrow{b}\hspace{0.06in}are\hspace{0.06in}parallel\hspace{0.06in}if\hspace{0.06in}\frac{a_{1}}{b_{1}}=\frac{a_{2}}{b_{2}}=\frac{a_{3}}{b_{3}}=\lambda ,\hspace{0.06in}[/laTEX][laTEX]where\hspace{0.06in}\overrightarrow{a}=a_{1}i+a_{2}j+a_{3}k\hspace{0.06in}\overrightarrow{b}=b_{1}i+b_{2}j+b_{3}k$[/laTEX]
But I have been told that we also get the same result even when the two vectors are collinear. Then, how do we know that if they are parallel or collinear? Two parallel straight lines have different y-axis intercepts if they are not collinear. What do you say? Thank you.
Regards
PG
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