The directions rations of two lines are 3,2,-6 and , 1,2,2 respectively . The acute
angle between these lines is
A. `cos ^(-1) .((5)/(18))`
B. `cos^(-1) .((3)/(20))`
C. `cos^(-1).((5)/(21))`
D. `cos^(-1)((8)/(21))`
angle between these lines is
A. `cos ^(-1) .((5)/(18))`
B. `cos^(-1) .((3)/(20))`
C. `cos^(-1).((5)/(21))`
D. `cos^(-1)((8)/(21))`
Correct Answer – C
cos `theta =(|(3xx1) +(2xx2)+(-6)xx2|)/({sqrt(3^(2) +2^(2) +(-6)^(2)}}{sqrt(1^(2)+2^(2)+2^(2))}}=(|-5|)/((sqrt(49)xxsqrt(49)))=(5)/((7xx3)) =(5)/(21)`
`=(1-51)/((sqrt(49)xxsqrt(49)))=(5)/((7xx3)) =(5)/(21)`
`rArr theta =cos^(-1) ((5)/(21))`