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Vector Algebra

Question
CBSEENMA12034027

If straight a with rightwards arrow on top and straight b with rightwards arrow on top are two collinear vectors, then which of the following are incorrect:

  • straight b with rightwards arrow on top equals space straight lambda space straight a with rightwards arrow on top comma space space for space some space scalar space straight lambda
  • straight a with rightwards arrow on top space equals plus-or-minus space straight b with rightwards arrow on top
  • the respective components of straight a with rightwards arrow on top space and space straight b with rightwards arrow on top are proportional

  • both the vectors straight a with rightwards arrow on top space and space straight b with rightwards arrow on top have same direction, but different magnitudes.

Solution

D.

both the vectors straight a with rightwards arrow on top space and space straight b with rightwards arrow on top have same direction, but different magnitudes.

Since straight a with rightwards arrow on top space and space straight b with rightwards arrow on top space are space two space collinear space vectors
therefore space space space space straight a with rightwards arrow on top space and space straight b with rightwards arrow on top space can space have space opposite space direction
therefore space space space space left parenthesis straight D right parenthesis space is space not space correct.