1
KCET 2025
MCQ (Single Correct Answer)
+1
-0

If $\vec{a}=\hat{i}+2 \hat{j}+\hat{k}, \vec{b}=\hat{i}-\hat{j}+4 \hat{k}$ and $\vec{c}=\hat{i}+\hat{j}+\hat{k}$ are such that $\vec{a}+\lambda \vec{b}$ is perpendicular to $\vec{c}$, then the value of $\lambda$ is

A
1
B
$\pm 1$
C
-1
D
0
2
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
3
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
4
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
$\sqrt{288}$
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