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Q.

In constructing a problem on vectors , the three components  of a vector are randomly chosen from the  digits 0 to 5 with replacement. The probability that the magnitude of vector is 5 is λ is then 12λ  =………..

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answer is 0.5.

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Detailed Solution

{0,1,2,3,4,5}=6n(s)=63r¯=xi¯+yj¯+3k¯|r¯|=5x2+y2+z2=5x2+y2+z2=25(5,0,0)3(3,4,0)3!=6P(A)=6+363=96.6.6=124=λ
12λ=12124=12=0.5

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