रेखाओं `(x-1)/(1) = (y +1)/(-2) = (z +2)/(1)` एवं `(x-1)/(1) = (2y +3)/(3) = (z + 5)/(2)` के बीच एक कोण क्या है ?

Options

A. `(pi)/(2)`
B. `(pi)/(3)`
C. `(pi)/(4)`
D. इनमे से कोई नहीं

Answer

A

Explanation

दी हुई रेखाएँ निम्न है,
`(x-2)/(1) = (y + 1)/(-2) = (z + 2)/(1) " "…(i)`
` (x-1)/(1) = (2y + 3)/(3) = (z + 5)/(2)`
`(x-1)/(1) = (2(y + (3)/(2)))/(3) = ( z + 5) /(2)`
`(x-1)/(1) = (y + 3//2)/(3//2) = (z + 5)/(2)" "...(ii)`
माना रेखा (i) तथा (ii) के बीच का कोण `theta` है |
`cos theta=|(1xx1+(-2)((3)/(2))+(2))/(sqrt(1 +(-2)^(2)+1^(2))sqrt(1^(2) + ((3)/(2))^(2)+2^(2)))|`
` =|(1 + (-3) +2)/(sqrt(1+4+1sqrt(1) + (9)/(4)+4))|=|(0)/(sqrt(6)sqrt((29)/(4)))|=0`
`therefore cos theta = 0 rArr cos theta = cos (pi)/(2) rArr theta = (pi)/(2)`