1
KCET 2025
MCQ (Single Correct Answer)
+1
-0
If $|\overrightarrow{\mathrm{a}}|=10,|\overrightarrow{\mathrm{~b}}|=2$ and $\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}=12$, then the value of $|\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}|$ is
A
5
B
10
C
14
D
16
2
KCET 2025
MCQ (Single Correct Answer)
+1
-0

Consider the following statements :

Statement (I) : If either $|\vec{a}|=0$ or $|\vec{b}|=0$, then $\vec{a} \cdot \vec{b}=0$

Statement (II) : If $\vec{a} \times \vec{b}=\overrightarrow{0}$, then a is perpendicular to $b$. Which of the following is correct?

A
Statement (I) is true but Statement (II) is false
B
Statement (I) is false but Statement (II) is true
C
Both Statement (I) and Statement (II) is true
D
Both Statement (I) and Statement (II) is false
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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