MHTCET 17 Apr 2026 Shift 1 Paper

Concept:The angle between two lines is obtained from the dot product of their direction vectors.Explanation:For the first line, take $\frac{x-1}{2}=\frac{2y+3}{4}=\lambda$ and $z=-2$.This gives $x=1+2\lambda$, $y=2\lambda-\frac{3}{2}$, and $z=-2$.So the direction ratios of the first line are $(2,2,0)$, which simplify to $(1,1,0)$.For the second line, take $x=1$ and $\frac{y-1}{2}=\frac{z+1}{2}=\mu$.This gives $y=1+2\mu$ and $z=-1+2\mu$.So the direction ratios of the second line are $(0,2,2)$, which simplify to $(0,1,1)$.Let $\vec{a}=(1,1,0)$ and $\vec{b}=(0,1,1)$.Using $\cos\theta=\frac{|\vec{a}\cdot\vec{b}|}{|\vec{a}||\vec{b}|}$:$\vec{a}\cdot\vec{b}=(1)(0)+(1)(1)+(0)(1)=1$.$|\vec{a}|=\sqrt{1^2+1^2+0^2}=\sqrt{2}$ and $|\vec{b}|=\sqrt{0^2+1^2+1^2}=\sqrt{2}$.Thus, $\cos\theta=\frac{1}{\sqrt{2}\cdot\sqrt{2}}=\frac{1}{2}$.Hence, $\theta=\frac{\pi}{3}$.Answer:$\theta=\frac{\pi}{3}$, which is Option B.