UPSC NDA Math Model Paper 9

Given: The direction ratios of two lines are (- 2, 1, 2) and (3, - 5, - 2)
As we know that, the angle between the lines with direction ratios <a1,b1,c1> and <a2,b2,c2> is given by: cos‌θ =

a1a2+b1b2+c1c2

√a12+b12+c12√a22+b22+c22

Here, a1=−2,b1=1,c1=2,a2=3,b2=−5 and c2=−2=−

5√38

38

⇒θ=cos−1(−

5√38

38

)
Hence, option A is the correct answer.