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Vector Algebra

Question
CBSEENMA12036236
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For any vector straight a with rightwards arrow on top  the value of left parenthesis straight a with rightwards arrow on top space straight x straight i with hat on top right parenthesis squared space plus left parenthesis straight a with rightwards arrow on top space straight x straight j with hat on top right parenthesis squared space plus left parenthesis straight a with rightwards arrow on top space straight x straight k with hat on top right parenthesis squared is equal to

  • 3 straight a with rightwards arrow on top squared
  • straight a with rightwards arrow on top squared
  • 2 straight a with rightwards arrow on top squared
  • 4 straight a with rightwards arrow on top squared

Solution

C.

2 straight a with rightwards arrow on top squared Let space straight a with rightwards arrow on top space equals space straight x straight i with hat on top plus straight y straight j with hat on top plus straight z straight k with hat on top straight a with rightwards arrow on top space straight x space straight i with hat on top space equals space straight z straight j with hat on top space minus space straight y straight k with hat on top rightwards double arrow left parenthesis straight a with rightwards arrow on top space straight x space straight i with hat on top right parenthesis squared space equals space straight y squared plus straight z squared rightwards double arrow left parenthesis straight a with rightwards arrow on top space straight x space straight j with hat on top right parenthesis space equals space straight x squared plus straight z squared rightwards double arrow left parenthesis straight a with rightwards arrow on top space straight x space straight k with hat on top right parenthesis space equals space straight x squared plus straight y squared similarly space left parenthesis straight a with rightwards arrow on top space straight x space straight j with hat on top right parenthesis squared space equals space straight x squared plus straight z squared and space open parentheses straight a with rightwards arrow on top space straight x stack space straight k with hat on top close parentheses squared space equals space straight x squared plus straight y squared rightwards double arrow space left parenthesis straight a with rightwards arrow on top space straight x space straight i with hat on top right parenthesis squared space plus space left parenthesis straight a with rightwards arrow on top space straight x straight j with hat on top right parenthesis squared space plus space left parenthesis straight a with hat on top space straight x straight k with hat on top right parenthesis squared space equals space 2 space left parenthesis straight x squared space plus straight y squared plus space straight z squared right parenthesis space equals space 2 straight a with rightwards arrow on top squared

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