If veca and vecb are two collinear vectors, then which of the following are incorrect:

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KollegeApply · Accepted Answer

Both the vectors veca and vecb have the same direction but different magnitudes. Explanation: If veca and vecb are two collinear vectors, then they are parallel. Therefore, we have: vecb = lambdaveca (For some scalar λ) If λ = $\pm$1, a = $\pm$b If `veca = a_1hati + a_2hatj + a_3hatk and vecb = b_1hati + b_2hatj + b_3hatk, then vecb = lambdaveca $\Rightarrow$ b_1hati + b_2hatj + b_3hatk = lambda(a_1hati + a_2hatj + a_3hatk) $\Rightarrow$ b_1hati + b_2hatj + b_3hatk = (lambdaa_1)hati + (lambdaa_2)hatj + (lambdaa_3)hatk $\Rightarrow$ b_1 = lambdaa_1, b_2 = lambdaa_2, b_3 = lambdaa_3 $\Rightarrow$ b_1/a_1 = b_2/a_2 = b_3/a_3 = lambda` Thus, the respective components of veca and vecb are proportional. However, vectors veca and vecb can have different directions. Hence, the statement given in D is incorrect.

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