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Asked by nranjith65001 22nd February 2021, 8:32 AM
Answered by Expert
Answer:
(a)  begin mathsize 14px style R with rightwards arrow on top subscript A B end subscript space equals space stack r subscript B with rightwards arrow on top space minus space r with rightwards arrow on top subscript A space equals space left parenthesis space 2 space stack a subscript x with rightwards arrow on top space plus space 2 space stack a subscript y with rightwards arrow on top plus 2 space stack a subscript z with rightwards arrow on top right parenthesis space minus space left parenthesis space minus space space stack a subscript x with rightwards arrow on top space minus 3 space space stack a subscript y with rightwards arrow on top space minus space 4 space space stack a subscript z with rightwards arrow on top space right parenthesis space equals space 3 space stack a subscript x with rightwards arrow on top space plus space 5 space stack a subscript y with rightwards arrow on top space plus 6 space stack a subscript z with rightwards arrow on top end style
 
(b) begin mathsize 14px style open vertical bar stack r subscript A with rightwards arrow on top close vertical bar space equals space square root of 1 plus 9 plus 16 end root space equals space square root of 26 end style
 
(c) begin mathsize 14px style a with rightwards arrow on top subscript A space equals negative space fraction numerator 1 over denominator square root of 26 end fraction open parentheses space a with rightwards arrow on top subscript x space plus space 3 space a with rightwards arrow on top subscript y space plus space 4 space a with rightwards arrow on top subscript z close parentheses end style

(d)

begin mathsize 14px style R with rightwards arrow on top subscript A B end subscript space equals space 3 space stack a subscript x with rightwards arrow on top space plus space 5 space stack a subscript y with rightwards arrow on top space plus 6 space stack a subscript z with rightwards arrow on top end style
begin mathsize 14px style open vertical bar R subscript A B end subscript close vertical bar space equals space square root of 9 plus 25 plus 36 end root space equals space square root of 70 end style
begin mathsize 14px style a with rightwards arrow on top subscript A B end subscript space equals fraction numerator 1 over denominator square root of 70 end fraction space open parentheses 3 space stack a subscript x with rightwards arrow on top space plus space 5 space stack a subscript y with rightwards arrow on top space plus 6 space stack a subscript z with rightwards arrow on top close parentheses end style
 
(e)

begin mathsize 14px style stack C A with rightwards arrow on top space equals space r with rightwards arrow on top subscript A space minus space r with rightwards arrow on top subscript C space equals space left parenthesis negative space a with rightwards arrow on top subscript x space minus 3 a with rightwards arrow on top subscript y space minus 4 a with rightwards arrow on top subscript z space right parenthesis space minus space left parenthesis space a with rightwards arrow on top subscript x space plus space 3 space a with rightwards arrow on top subscript x space plus space 4 a with rightwards arrow on top subscript x space right parenthesis space equals space minus 2 space a with rightwards arrow on top subscript x space minus space 6 space a with rightwards arrow on top subscript y space minus space 8 a with rightwards arrow on top subscript z end style
 
begin mathsize 14px style open vertical bar stack C A with rightwards arrow on top close vertical bar space equals space square root of 4 plus 36 plus 64 end root space equals space 2 square root of 26 end style
begin mathsize 14px style a with rightwards arrow on top subscript C A end subscript space space equals negative fraction numerator 1 over denominator square root of 26 end fraction open parentheses a with rightwards arrow on top subscript x space plus 3 space a with rightwards arrow on top subscript y space plus 4 a with rightwards arrow on top subscript z close parentheses space end style
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Answered by Expert 22nd February 2021, 1:08 PM
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