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Vector Algebra

Question
CBSEENMA12034272
Wired Faculty App

Area of a rectangle having vertices A, B, C and D with position vectors
negative straight i with hat on top space plus space 1 half straight j with hat on top space plus space 4 space straight k with hat on top comma space space space straight i with hat on top space plus space 1 half straight j with hat on top space plus space 4 space straight k with hat on top comma space space space space straight i with hat on top space minus space 1 half straight j with hat on top space plus 4 straight k with hat on top space and space minus straight i with hat on top space minus space 1 half straight j with hat on top space plus space 4 straight k with hat on top comma respectively is
  • 1 half

  • 1

  • 2

  • 4

Solution

C.

2

Position vectors of vertices A, B, C, D of rectangle are
negative straight i with hat on top space plus space 1 half straight j with hat on top space plus space 4 space straight k with hat on top comma space space space straight i with hat on top space plus space 1 half straight j with hat on top space plus space 4 space straight k with hat on top comma space space space space straight i with hat on top space minus space 1 half straight j with hat on top space plus 4 straight k with hat on top space and space minus straight i with hat on top space minus space 1 half straight j with hat on top space plus space 4 straight k with hat on top comma respectively                 therefore space space space AB with rightwards arrow on top space equals space straight P. straight V. space of space straight B space minus space straight P. straight V. space of space straight A space equals space open parentheses straight i with hat on top space plus space 1 half straight j with hat on top space plus space 4 space straight k with hat on top close parentheses space minus space open parentheses negative straight i with hat on top space plus space 1 half straight j with hat on top space plus space 4 space straight k with hat on top close parentheses space equals space 2 space straight i with hat on top
  space and space AD with rightwards arrow on top space equals space straight P. straight V. space of space straight D space minus space straight P. straight V. space of space straight A space space space space space space equals space open parentheses negative straight i with hat on top space minus space 1 half straight j with hat on top space plus space 4 space straight k with hat on top close parentheses space minus space open parentheses negative straight i with hat on top space plus space 1 half straight j with hat on top space plus space 4 space straight k with hat on top close parentheses space equals space minus straight j with hat on top AB with rightwards arrow on top space cross times space AD with rightwards arrow on top space equals space 2 space straight i with hat on top space cross times space left parenthesis negative straight j with hat on top right parenthesis space equals space minus 2 space left parenthesis straight i with hat on top space cross times space straight j with hat on top right parenthesis space equals space minus 2 space straight k with hat on top therefore space space area space of space rectangle space space equals space open vertical bar AB with rightwards arrow on top space cross times space AD with rightwards arrow on top close vertical bar space equals space left parenthesis negative 2 space straight k with hat on top right parenthesis space equals space 2 therefore space space left parenthesis straight C right parenthesis space is space correct space answer.

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