If the two lines l1: x-2/3 = y + 2/-2, z = 2 and l2 : x - 1/1 = 2y + 3/α = z + 5/2 perpendicular, then an angle between the lines

Question

If the two lines \(l_1:\frac{x-2}3=\frac{y+1}{-2}, z = 2\) and \(l_2:\frac{x-1}1=\frac{2y+3}{\alpha}=\frac{z+5}2\) perpendicular, then an angle between the lines l₂ and \(l_3:\frac{1-x}3=\frac{2y-1}{-4}=\frac z4\) is :

(A) cos^-1 (29/4)

(B) sec^-1 (29/4)

(C) cos^-1(2/29)

(D) cos^-1(2/√29)

Answer 1

Correct option is (B) sec^-1 (29/4)

θ = cos^-1(4/29) ⇒ θ = sec^-1(29/4)