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1
KCET 2026
MCQ (Single Correct Answer)
+1
-0
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
A
$\cos^{-1}\left(\dfrac{2}{3}\right)$
B
$\cos^{-1}\left(\sqrt{\dfrac{2}{3}}\right)$
C
$\cos^{-1}\left(\sqrt{\dfrac{3}{2}}\right)$
D
$\cos^{-1}\left(\dfrac{3}{2}\right)$
2
KCET 2026
MCQ (Single Correct Answer)
+1
-0
The angle between the lines whose direction ratios are $a, b, c$ and $b - c, c - a, a - b$ is
A
$90^\circ$
B
$60^\circ$
C
$30^\circ$
D
$0^\circ$
3
KCET 2025
MCQ (Single Correct Answer)
+1
-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

A
$\frac{\pi}{6}$
B
$\frac{\pi}{4}$
C
$\frac{\pi}{3}$
D
$\frac{\pi}{2}$
4
KCET 2025
MCQ (Single Correct Answer)
+1
-0

The equation of the line through the point $(0,1,2)$ and perpendicular to the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{-2}$ is

A
$\frac{x}{3}=\frac{y-1}{4}=\frac{z-2}{-3}$
B
$\frac{\mathrm{x}}{-3}=\frac{\mathrm{y}-1}{4}=\frac{\mathrm{z}-2}{3}$
C
$\frac{x}{3}=\frac{y-1}{4}=\frac{z-2}{3}$
D
$\frac{x}{3}=\frac{y-1}{-4}=\frac{z-2}{3}$
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