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text  If  end text a with not stretchy bar on top equals ı with not stretchy bar on top plus 2 ȷ with not stretchy bar on top plus 3 k with not stretchy bar on top comma b with not stretchy bar on top equals negative ı with not stretchy bar on top plus 2 ȷ with not stretchy bar on top plus k with not stretchy bar on top comma c with not stretchy bar on top equals 3 ı with not stretchy bar on top plus ȷ with not stretchy bar on top text  and  end text a with not stretchy bar on top plus t b with not stretchy bar on top is perpendicular to stack c with ‾ on top, then t equals

  1. 5    
  2. 4    
  3. 3    
  4. 2    

hintHint:

We are given three vectors We are given that  vector a with bar on top plus t b with rightwards arrow on top and c with rightwards arrow on top are perpendicular. We have to find the value of t. We will first find the value of a with rightwards arrow on top plus t b with rightwards arrow on top.

The correct answer is: 5


    The given vectors are a with rightwards arrow on top equals i with hat on top plus 2 j with hat on top plus 3 k with hat on topnegative i with hat on top plus 2 j with hat on top plus k with hat on top and 3 i with hat on top plus j with hat on top
    We have to find out a with rightwards arrow on top plus t b with rightwards arrow on top
    We are given that the vector a with rightwards arrow on top plus t b with rightwards arrow on top and c with rightwards arrow on top are perpendicular. So, their dot product will be zero.
    Taking the dot product
    open parentheses a with rightwards arrow on top plus t b with rightwards arrow on top close parentheses. c with rightwards arrow on top equals 0
left square bracket i with hat on top space plus space 2 j with hat on top space plus space 3 k with hat on top space plus space t left parenthesis negative i with hat on top space plus space 2 j with hat on top space plus space k with hat on top right parenthesis. space left parenthesis 3 i with hat on top plus j with hat on top right parenthesis space equals space 0
space left parenthesis left parenthesis 1 space minus t right parenthesis i with hat on top space plus space left parenthesis 2 space plus 2 t right parenthesis j with hat on top space plus space left parenthesis 3 space plus space t right parenthesis k with hat on top right parenthesis. left parenthesis 3 i with hat on top plus j with hat on top right parenthesis space equals space 0
space space space space space 3 left parenthesis 1 space minus t right parenthesis space plus space left parenthesis 2 space plus space 2 t right parenthesis space equals space 0
space space space space space space space 3 space minus space 3 t space plus space 2 space plus space 2 t space equals space 0
space space space space space space space space 5 space minus space t space equals space 0
space space space space space space space space space space space t space equals space 5
    So, the value of t is 5.

    For this question, we should know the rules of dot product.

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