KCET 2026 | Three Dimensional Geometry Question 1 | Mathematics

The measure of the angle between the lines $x = k + 1, y = 2k - 1, z = 2k + 3, k \in \mathbb{R}$ and $\dfrac{x - 1}{2} = \dfrac{y - 2}{1} = \dfrac{z - 3}{1}$ is

$\cos^{-1}\left(\dfrac{2}{3}\right)$

$\cos^{-1}\left(\sqrt{\dfrac{2}{3}}\right)$

$\cos^{-1}\left(\sqrt{\dfrac{3}{2}}\right)$

$\cos^{-1}\left(\dfrac{3}{2}\right)$

KCET 2026

MCQ (Single Correct Answer)

-0

The angle between the lines whose direction ratios are $a, b, c$ and $b - c, c - a, a - b$ is

$90^\circ$

$60^\circ$

$30^\circ$

$0^\circ$

KCET 2025

MCQ (Single Correct Answer)

-0

If a line makes angles $90^{\circ}, 60^{\circ}$ and $\theta$ with $\mathrm{x}, \mathrm{y}$ and z axes respectively, where $\theta$ is acute, then the value of $\theta$ is

$\frac{\pi}{6}$

$\frac{\pi}{4}$

$\frac{\pi}{3}$

$\frac{\pi}{2}$

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