If |→a|=∣∣→b∣∣=|→c|=3 and →a.→b.=→b.→c=→c.→a=4. If →p,→q,→r is the reciprocal system of →a,→b,→c, then 85[→p→q→r] is equal to
A
√17
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B
2√17
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C
3√17
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D
5√17
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Solution
The correct option is C√17 We take
[¯¯¯a¯¯b¯¯c]2=∣∣
∣
∣∣¯a,.¯a¯a.¯b¯a.¯c¯b.¯a¯b.¯b¯b.¯c¯c.¯a¯c.¯b¯c.¯c∣∣
∣
∣∣ =∣∣
∣∣944494449∣∣
∣∣=425 [¯¯¯a¯¯b¯¯c]=5√17 For the reciprocal system , the property is [¯¯¯p¯¯¯q¯¯¯r][¯¯¯a¯¯b¯¯c]=1 [¯¯¯p¯¯¯q¯¯¯r]=15√17 85[¯¯¯p¯¯¯q¯r]=√17