If L1 and L2 have the direction ratios (a_1,b_1,c_1 ,and ,a_2,b_2,c_2 ) respectively then what is the angle between the lines?

Question

If L1 and L2 have the direction ratios  (a_1,b_1,c_1  ,and  ,a_2,b_2,c_2 ) respectively then what is the angle between the lines?

TuteeHUB · Accepted Answer

( =2   ,cos^{-1} u2061  left|  frac{a_1 a_2+b_1 b_2+c_1 c_2}{  sqrt{a_1^2+b_1^2+c_1^2}   sqrt{a_2^2+b_2^2+c_2^2}}  right |  )

TuteeHUB · Answer

( =tan^{-1} u2061  left|  frac{a_1 a_2+b_1 b_2+c_1 c_2}{  sqrt{a_1^2+b_1^2+c_1^2}   sqrt{a_2^2+b_2^2+c_2^2}}  right |  )

TuteeHUB · Answer

( =2tan^{-1} u2061  left|  frac{a_1 a_2+b_1 b_2+c_1 c_2}{  sqrt{a_1^2+b_1^2+c_1^2}   sqrt{a_2^2+b_2^2+c_2^2}}  right |  )

TuteeHUB · Answer

( =cos^{-1} u2061  left|  frac{a_1 a_2+b_1 b_2+c_1 c_2}{  sqrt{a_1^2+b_1^2+c_1^2}   sqrt{a_2^2+b_2^2+c_2^2}}  right |  )

TuteeHUB · Answer

( =2   ,cos^{-1} u2061  left|  frac{a_1 a_2+b_1 b_2+c_1 c_2}{  sqrt{a_1^2+b_1^2+c_1^2}   sqrt{a_2^2+b_2^2+c_2^2}}  right |  )

1.	If L₁ and L₂ have the direction ratios (a_1,b_1,c_1 ,and ,a_2,b_2,c_2 ) respectively then what is the angle between the lines?
A.	( =tan^{-1} u2061 left\| frac{a_1 a_2+b_1 b_2+c_1 c_2}{ sqrt{a_1^2+b_1^2+c_1^2} sqrt{a_2^2+b_2^2+c_2^2}} right \| )
B.	( =2tan^{-1} u2061 left\| frac{a_1 a_2+b_1 b_2+c_1 c_2}{ sqrt{a_1^2+b_1^2+c_1^2} sqrt{a_2^2+b_2^2+c_2^2}} right \| )
C.	( =cos^{-1} u2061 left\| frac{a_1 a_2+b_1 b_2+c_1 c_2}{ sqrt{a_1^2+b_1^2+c_1^2} sqrt{a_2^2+b_2^2+c_2^2}} right \| )
D.	( =2 ,cos^{-1} u2061 left\| frac{a_1 a_2+b_1 b_2+c_1 c_2}{ sqrt{a_1^2+b_1^2+c_1^2} sqrt{a_2^2+b_2^2+c_2^2}} right \| )
Answer» D. ( =2 ,cos^{-1} u2061 left\| frac{a_1 a_2+b_1 b_2+c_1 c_2}{ sqrt{a_1^2+b_1^2+c_1^2} sqrt{a_2^2+b_2^2+c_2^2}} right \| )

If L₁ and L₂ have the direction ratios (a_1,b_1,c_1 ,and ,a_2,b_2,c_2 ) respectively then what is the angle between the lines?