1
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
2
KCET 2024
MCQ (Single Correct Answer)
+1
-0

The vectors $\mathbf{A B}=3 \hat{\mathbf{i}}+4 \hat{\mathbf{k}}$ and $\mathbf{A C}=5 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$ are the sides of a $\triangle A B C$, The length of the median through $A$ is

A
$\sqrt{18}$
B
$\sqrt{72}$
C
$\sqrt{33}$
D
$\sqrt{288}$
3
KCET 2024
MCQ (Single Correct Answer)
+1
-0

The volume of the parallelopiped whose co terminous edges are $\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+\hat{\mathbf{j}}$ is

A
6 cu units
B
2 cu units
C
4 cu units
D
3 cu units
4
KCET 2024
MCQ (Single Correct Answer)
+1
-0

Let $\mathbf{a}$ and $\mathbf{b}$ be two unit vectors and $\theta$ is the angle between them. Then, $\mathbf{a}+\mathbf{b}$ is a unit vector, if

A
$\theta=\frac{\pi}{4}$
B
$\theta=\frac{\pi}{3}$
C
$\theta=\frac{2 \pi}{3}$
D
$\theta=\frac{\pi}{2}$
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