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Vector Algebra

Question
CBSEENMA12036098
Wired Faculty App

The vector straight a with rightwards arrow on top space and space straight b with rightwards arrow on top are not perpendicular  and straight c with rightwards arrow on top space and space straight d with rightwards arrow on top are two vectors satisfying: straight b with rightwards arrow on top space straight x straight c with rightwards arrow on top space equals space straight b with rightwards arrow on top space straight x straight d with rightwards arrow on top space and space straight a with rightwards arrow on top. straight b with rightwards arrow on top space equals space 0. The vector straight d with rightwards arrow on top is equal to

  • straight b with rightwards arrow on top space minus space open parentheses fraction numerator straight b. straight c over denominator straight a with rightwards arrow on top. straight d with rightwards arrow on top end fraction close parentheses straight c with rightwards arrow on top
  • straight c with rightwards arrow on top space plus open parentheses fraction numerator straight a with rightwards arrow on top. straight c with rightwards arrow on top over denominator straight a with rightwards arrow on top. straight b with rightwards arrow on top end fraction close parentheses straight b with rightwards harpoon with barb upwards on top
  • straight b with rightwards arrow on top space plus space open parentheses fraction numerator straight b with rightwards arrow on top. straight c with rightwards arrow on top over denominator straight a with rightwards arrow on top. straight b with rightwards arrow on top end fraction close parentheses straight c with rightwards arrow on top
  • straight c with rightwards arrow on top minus open parentheses fraction numerator straight a with rightwards arrow on top. straight c with rightwards arrow on top over denominator straight a with rightwards arrow on top. straight b with rightwards arrow on top end fraction close parentheses straight b with rightwards arrow on top

Solution

D.

straight c with rightwards arrow on top minus open parentheses fraction numerator straight a with rightwards arrow on top. straight c with rightwards arrow on top over denominator straight a with rightwards arrow on top. straight b with rightwards arrow on top end fraction close parentheses straight b with rightwards arrow on top straight a with rightwards arrow on top. straight b with rightwards arrow on top space not equal to space 0 comma space straight b with rightwards arrow on top space straight x straight d with rightwards arrow on top space comma straight a with rightwards arrow on top. straight d with rightwards arrow on top space equals space 0 left parenthesis straight b with rightwards arrow on top space straight x space straight c with rightwards arrow on top right parenthesis space space straight x space straight a with rightwards arrow on top space equals space left parenthesis straight b with rightwards arrow on top space straight x space straight d with rightwards arrow on top space right parenthesis space space straight x space straight a with rightwards arrow on top left parenthesis straight b with rightwards arrow on top. straight a with rightwards arrow on top right parenthesis straight c with rightwards arrow on top space minus space left parenthesis straight c with rightwards arrow on top. straight a with rightwards arrow on top right parenthesis straight b with rightwards arrow on top space equals space straight b with rightwards arrow on top. straight a with rightwards arrow on top right parenthesis straight b with rightwards arrow on top space minus left parenthesis straight d with rightwards arrow on top. straight a with rightwards arrow on top right parenthesis straight b with rightwards arrow on top straight d with rightwards arrow on top space equals straight c with rightwards arrow on top space minus space open parentheses fraction numerator straight a with rightwards arrow on top. straight c with rightwards arrow on top over denominator straight a with rightwards arrow on top. straight b with rightwards arrow on top end fraction close parentheses straight b with rightwards arrow on top

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