Question

If \(θ\) is the angle between the lines \(\frac{x-1}{2} = \frac{2y+3}{4}; z = -2\) and \(x = 1; \frac{y-1}{2} = \frac{z+1}{2}\), then

• A. \(θ = \frac{π}{6}\)
• B. \(θ = \frac{π}{3}\)
• C. \(θ = \frac{π}{4}\)
• D. \(θ = \frac{π}{2}\)

Hint:

Find the direction ratios and use the dot product formula.

Answer 1

The Correct Option is B

Step 1: Write direction vectors
$\vec d_1=(1,1,0)$ and $\vec d_2=(0,1,1)$.

Step 2: Compute
$\vec d_1\cdot\vec d_2=1$ and $|\vec d_1||\vec d_2|=2$, so $\cos\theta=\tfrac12$ and $\theta=60^{\circ}$, option (B).

Final Answer:
The angle is $60^{\circ}$, option (B). \[ \boxed{\dfrac\pi3} \]