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Vector Algebra

Question
CBSEENMA12036277
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A particle is acted upon by constant forces 4 space straight i with hat on top space plus straight j with hat on top space minus 3 straight k with hat on top space space and 3 space straight i with hat on top space plus straight j with hat on top space minus straight k with hat on top which displace it from a point straight i with hat on top space plus 2 straight j with hat on top space plus 3 straight k with hat on top space to space the space point space 5 straight i with hat on top space plus space 4 straight j with hat on top space plus straight k with hat on top. space The work done in standard units by the forces is given by 

  • 40

  • 30

  • 25

  • 15

Solution

A.

40

work space done space by space the space forces space stack straight F subscript 1 with rightwards arrow on top space and space stack straight F subscript 2 with rightwards arrow on top space is space left parenthesis straight F with rightwards arrow on top subscript 1 space plus space stack straight F subscript 2 with rightwards arrow on top right parenthesis. straight d with rightwards arrow on top comma space where space straight d with rightwards arrow on top space is space displacement According space to space question space stack straight F subscript 1 with rightwards arrow on top space plus stack straight F subscript 2 with rightwards arrow on top space equals space left parenthesis 4 straight i with hat on top space plus straight j with hat on top minus 3 straight k with hat on top right parenthesis space plus space left parenthesis 3 straight i with hat on top space plus straight j with hat on top minus straight k with hat on top right parenthesis space equals space 7 straight i with hat on top space plus 2 straight j with hat on top space minus 4 straight k with hat on top and space straight d with rightwards arrow on top space equals left parenthesis 5 straight i with hat on top space plus 4 straight j with hat on top space plus straight k with hat on top right parenthesis space minus space left parenthesis straight i with hat on top space plus 2 straight j with hat on top space plus 3 straight k with hat on top right parenthesis space equals space 4 straight i with hat on top space plus 2 straight j with hat on top space minus 2 straight k with hat on top. Hence space left parenthesis stack straight F subscript 1 space with rightwards arrow on top space plus straight F with rightwards arrow on top subscript 2 right parenthesis. space straight d space is space 40

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work done

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