Correct Answer - Option 2 :
\(\dfrac{\pi}{4}\)
CONCEPT:
The angle θ between two lines whose direction ratios are proportional to a1, b1, c1 and a2, b2, c2 respectively is given by: \(\cos θ = \left| {\frac{{{a_1}{a_2} + {b_1}{b_2} + {c_1}{c_2}}}{{\sqrt {a_1^2 + b_1^2 + c_1^2} \;\sqrt {a_2^2 + b_2^2 + c_2^2} }}} \right|\)
CALCULATION:
Here, we have to find the angle between the two lines having direction ratios (6, 3, 6) and (3, 3, 0).
Here, a1 = 6, b1 = 3, c1 = 6, a2 = 3, b2 = 3 and c2 = 0
As we know that, if θ is the angle between two lines having direction ratios proportional to a1, b1, c1 and a2, b2, c2 is given by: \(\cos θ = \left| {\frac{{{a_1}{a_2} + {b_1}{b_2} + {c_1}{c_2}}}{{\sqrt {a_1^2 + b_1^2 + c_1^2} \;\sqrt {a_2^2 + b_2^2 + c_2^2} }}} \right|\)
⇒ \(\cos θ = \left| {\frac{{6 \cdot 3 + 3 \cdot 3 +6 \cdot 0}}{{\sqrt {6^2 + 3^2 + 6^2} \;\sqrt {3^2 + 3^2 + 0^2} }}} \right|\)
⇒ \(cos θ = \frac{1}{\sqrt 2}\)
⇒ θ = π/4
Hence, correct option is 2.