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Vector Algebra

Question
CBSEENMA12036184
Wired Faculty App

Let space straight a with minus on top space equals space straight i with hat on top space plus straight j with hat on top space plus straight k comma space straight b with bar on top space equals space straight i with hat on top space minus straight j with hat on top space plus 2 straight k with hat on top space and space straight c with bar on top space equals space straight x straight i with hat on top space plus space left parenthesis straight x minus 2 right parenthesis straight j with hat on top minus straight k with hat on top. If space the space vector space straight c with bar on top space lies space in space the space plane space of space straight a with bar on top space and space straight b with bar on top comma space then space straight x space equals

  • 0

  • -1

  • -2

  • -4

Solution

C.

-2

straight a with rightwards arrow on top space equals space straight i with hat on top space plus straight j with hat on top space plus straight k with hat on top straight b with rightwards arrow on top space equals space straight i with hat on top space minus straight j with hat on top space plus 2 straight k with hat on top straight c with rightwards arrow on top space equals space straight x straight i with hat on top space plus left parenthesis straight x minus 2 right parenthesis straight j with hat on top space minus straight k with hat on top open vertical bar table row straight x cell straight x minus 2 end cell cell negative 1 end cell row 1 1 1 row 1 cell negative 1 end cell 2 end table close vertical bar space equals 0 3 straight x plus 2 space minus straight x plus 2 space equals 0 2 straight x equals negative 4 straight x equals negative 2

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