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Q19 If $\vec{a}$ and $\vec{b}$ are two collinear vectors, then which of the following is incorrect:
(A) $\vec{b}=\lambda \vec{a}$ for some scalar $\lambda$
(B) $\vec{a}= \pm \vec{b}$
(C) the respective components of $\vec{a}$ and $\vec{b}$ are not proportional
(D) both the vectors $\vec{a}$ and $\vec{b}$ have the same direction, but different magnitudes.
Answers (1)
(A) If two vectors are collinear then, they have the same direction or are parallel or antiparallel.Therefore, They can be expressed in the form $\vec{b}=\lambda \vec{a}$ where a and b are vectors and $\lambda$ is some scalar quantity. Therefore, (A) is true.
(B) $\lambda$ is a scalar quantity so its value may be equal to $\pm 1$ is the obvious result. Therefore, (B) is also true.
(C) The vectors $\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{b}}$ are proportional, Therefore, (C) is not true.
(D) The vectors $\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{b}}$ can have different magnitudes as well as different directions. Therefore, (D) is not true.
Therefore, the incorrect options are (C) and (D).
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