NDA Math Three Dimensional Geometry

CONCEPT:
The angle θ between two lines whose direction ratios are proportional to a1,b1,c1 and a2,b2,c2 respectively is given by: cos‌θ=|‌

a1a2+b1b2+c1c2

√a12+b12+c12√a22+b22+c22

|
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 directionratios proportional to a1,b1,c1 and a2,b2,c2 is given by:
cos‌θ=|‌

a1a2+b1b2+c1c2

√a12+b12+c12√a22+b22+c22

|
⇒cos‌θ=|‌

6⋅3+3⋅3+6⋅0

√62+32+62√32+32+02

|
⇒cos‌θ=‌

1

√2

⇒θ=π∕4
Hence, correct option is 2.