COMEDK 2024 Shift 2 Paper

To determine the measure of the angle between the given lines, we need to compare their direction vectors. Let's analyze each line individually.
The first line is given by the parametric equations:
x=k+1,‌‌y=2k−1,‌‌z=2k+3,‌‌k∈ℝ
We can rewrite the parametric equations to identify the direction vector. Let's denote the direction vector of this line as d1. By taking the difference for a unit increment in parameter k, we get:
The second line is given in symmetric form:
‌

x−1

2

=‌

y+1

1

=‌

z−1

−2

From this form, we can identify the direction vector d2 directly as:
d2=⟨2,1,−2⟩
To find the angle θ between the two lines, we use the dot product formula for the direction vectors:
cos‌θ=‌

d1⋅d2

|d1||d2|

First, compute the dot product d1⋅d2 :
Since the dot product is 0 , it indicates that the vectors are orthogonal. Therefore, the angle between the two lines is:
θ=‌

π

2

Hence, the correct option is:
Option D ‌

π

2