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Vector Algebra

Question
CBSEENMA12036279
Wired Faculty App

Let straight u with bar on top comma space straight v with bar on top space comma space straight w with bar on top be such that vertical line top enclose straight u vertical line space equals space vertical line top enclose straight v vertical line space equals space 2 comma space vertical line top enclose straight w vertical line space equals space 3 If the projection top enclose straight v space along space top enclose straight u  is equal to that of space top enclose straight w space along space top enclose top enclose straight u end enclose space and space top enclose straight v comma space top enclose straight w space are perpendicular to each other then vertical line top enclose straight u space minus top enclose straight v space plus top enclose straight w vertical line equals

  • 2

  • square root of 14
  • square root of 12

  • 12

Solution

B.

square root of 14 vertical line top enclose straight u vertical line space equals space 1 comma space vertical line top enclose straight v vertical line space equals space 2 comma space vertical line top enclose straight w vertical line space equals space 3 projection space of space top enclose straight v space along space straight u with rightwards arrow on top space equals fraction numerator straight v with rightwards arrow on top. straight u with rightwards arrow on top over denominator vertical line top enclose straight u vertical line end fraction projection space of space top enclose straight u space along space straight w with rightwards arrow on top space equals space fraction numerator straight w with rightwards arrow on top. straight u with rightwards arrow on top over denominator vertical line straight u with rightwards arrow on top vertical line end fraction rightwards double arrow stack straight v. with rightwards arrow on top straight u with rightwards arrow on top space equals space straight w with rightwards arrow on top. straight u with rightwards arrow on top and space straight v with rightwards arrow on top comma straight w with rightwards arrow on top space are space perpendicular space to space each space other therefore space straight v with rightwards arrow on top comma straight w with rightwards arrow on top space equals space 0 vertical line straight u with rightwards arrow on top minus straight v with rightwards arrow on top space plus straight w with rightwards arrow on top vertical line squared space equals space vertical line straight u with rightwards arrow on top vertical line squared space plus space vertical line straight v with rightwards arrow on top vertical line squared space plus vertical line straight w with rightwards arrow on top vertical line squared space minus 2 straight u with rightwards arrow on top. straight v with rightwards arrow on top space plus 2 straight u with rightwards arrow on top. straight w with rightwards arrow on top space minus space 2 straight v with rightwards arrow on top. straight w with rightwards arrow on top vertical line straight u with rightwards arrow on top minus straight v with rightwards arrow on top space plus straight w with rightwards arrow on top vertical line squared space space equals space 1 plus 4 plus 9 space minus 2 straight u with rightwards arrow on top. straight v with rightwards arrow on top space plus 2 straight v with rightwards arrow on top space. straight u with rightwards arrow on top vertical line straight u with rightwards arrow on top minus straight v with rightwards arrow on top space plus straight w with rightwards arrow on top vertical line squared space equals space 1 plus 4 plus 9 vertical line straight u with rightwards arrow on top minus straight v with rightwards arrow on top space plus straight w with rightwards arrow on top vertical line squared space equals space square root of 14

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work done

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