रेखा -युग्म :
`" " (x + 3 )/(3 ) = ( y - 1)/(5) = (z + 3)/(4)`
और `" " (x + 1)/(1) = ( y - 4)/(1) = (z - 5)/(2)`
के मध्य कोण ज्ञात कीजिए |

Find the S.D. between the lines : (i) (x)/(2) = (y)/(-3) = (z)/(1) and (x -2)/(3) = (y - 1)/(-5) = (z + 4)/(2) (ii) (x -1)/(2) = (y - 2)/(3) = (z - 3)/(2) and (x + 1)/(3) = (y - 1)/(2) = (z - 1)/(5) (iii) (x + 1)/(7) = (y + 1)/(-6) = (z + 1)/(1) and (x -3)/(1) = (y -5)/(-2) = (z - 7)/(1) (iv) (x - 3)/(3) = (y - 8)/(-1) = (z-3)/(1) and (x + 3)/(-3) = (y +7)/(2) = (z -6)/(4) .

Show that the line (x+3)/(2) = (y+1)/(-1) = (z+3)/(3) and (x)/(5) = (y-5)/(1) = (z-3)/(-3) are perpendicular.

Show that the lines : (i) (x -5)/(7) = (y + 2)/(-5) = (z)/(1) " " and (x)/(1) = (y)/(2) = (z)/(3) (ii) (x - 3)/(2) = (y + 1)/(-3) = (z - 2)/(4) and (x + 2)/(2) = (y - 4)/(4) = (z + 5)/(2) are perpendicular to each other .

Find the value of (( x -y )^3 + ( y - z )^3 + ( z - x )^3 )/ (9 ( x - y )( y - z ) ( z - x )) 1 . 0 2 . 1/9 3 . 1/3 4. 1

If (x + y) ^((1)/(3)) + (y + x) ^((1)/(3)) =- ( z + x ) ^((1)/(3)) , then (x ^(3) + y ^(3) + z ^(3)) can be expressed as :

" The point of intersection of lines "(x-1)/(2)=(y-2)/(3)=(z-3)/(4)" and "(x-4)/(5)=(y-1)/(2)=(z)/(1)" is "