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+1 vote
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If   \(\vec a\)  and  \(\vec b\) are two collinear vectors, then which of the following are incorrect ?

A. \(\vec b=\lambda\,\vec a\) for some scalar λ

B. \(\vec a=\pm\vec b\)

C. the respective components of  \(\vec a\) and  \(\vec b\) are proportional

D. both the vectors  \(\vec a\) and  \(\vec b\) have the same direction but different magnitudes.

1 Answer

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by (28.8k points)
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Best answer

If  \(\vec a\) &  \(\vec b\) are collinear vectors, then they are parallel.

Then, \(\vec b=\lambda\vec a\)

For some scalar \(\lambda\)

If  \(\lambda\) = \(\pm1,\) then,

Thus, respective components of  \(\vec a \) &  \(\vec b\) are proportional.

However the vectors  \(\vec a \) &  \(\vec b\) can have different directions.

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