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Vector Algebra

Question
CBSEENMA12036197
Wired Faculty App

If space left parenthesis top enclose straight a space straight x space top enclose straight b right parenthesis space straight x space top enclose straight c space equals space top enclose straight a space straight x space left parenthesis top enclose straight b space straight x space top enclose straight c right parenthesis comma space where space top enclose straight a comma space top enclose straight b space and space top enclose straight c space are any three vectors such that top enclose straight a. top enclose straight b space not equal to 0 space top enclose straight b. top enclose straight c space not equal to 0 comma space then space straight a with bar on top space and space straight c with bar on top space are

  • inclined at an angle of π/3 between them

  • inclined at an angle of π/6 between them

  • perpendicular

  • parallel

Solution

D.

parallel

left parenthesis top enclose straight a space straight x space top enclose straight b right parenthesis space straight x top enclose straight c space equals space top enclose straight a space straight x space left parenthesis top enclose straight b space straight x top enclose straight c right parenthesis comma space top enclose straight a. top enclose straight b space not equal to 0 comma space straight b with rightwards arrow on top. straight c with rightwards arrow on top space not equal to 0 rightwards double arrow space left parenthesis top enclose straight a. top enclose straight c right parenthesis. top enclose straight b space minus left parenthesis top enclose straight b. top enclose straight c right parenthesis top enclose straight a space equals space left parenthesis top enclose straight a. top enclose straight c right parenthesis top enclose straight b space minus left parenthesis top enclose straight a. top enclose straight b right parenthesis top enclose straight c left parenthesis top enclose straight a. top enclose straight b right parenthesis top enclose straight c space equals left parenthesis top enclose straight b. top enclose straight c right parenthesis top enclose straight a top enclose straight a space vertical line vertical line top enclose straight c

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