UPSC NDA Math Model Paper 6

Given: The direction ratios of two lines are (2, 3, 6) and (1, 2, 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=3,c1=6,a2=1,b2=2 and c2=2
⇒cos‌θ=

2×1+3×2+6×2

√22+32+62×√12+22+22

=

20

21

⇒θ=cos−1(

20

21

)
Hence, option A is the correct answer.