1
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If two vectors $\mathbf{a}$ and $\mathbf{b}$ which are perpendicular to each other are such that $|\mathbf{a}|=8$ and $|\mathbf{b}|=3$, then $|\mathbf{a}-2 b|=$

A
10
B
2
C
6
D
12
2
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

Let $\mathbf{a}$ and $\mathbf{b}$ be non-collinear vectors. If the vectors $(\lambda-1) \mathbf{a}+2 \mathbf{b}$ and $3 \mathbf{a}+\lambda \mathbf{b}$ are collinear, then the set of all possible values of $\lambda$ is

A
$\{2,3\}$
B
$\{-2,3\}$
C
$\{-2,-3\}$
D
$\{2,-3\}$
3
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

Vectors $\mathbf{p}=a \hat{\mathbf{i}}+b \hat{\mathbf{j}}+c \hat{\mathbf{k}}, \mathbf{q}=d \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$ and $\mathbf{r}=3 \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ forming a $\triangle A B C$ are such that $\mathbf{p}=\mathbf{q}+\mathbf{r}$. If the area of $\triangle A B C$ is $5 \sqrt{6}$ sq. units, then the sum of the absolute values of $a, b, c$ is

A
14
B
13
C
12
D
10
4
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

$\mathbf{b}$ and $\mathbf{c}$ are non-collinear vectors and $(\mathbf{c} \cdot \mathbf{c}) \mathbf{a}=\mathbf{c}$. If $(\mathbf{a} \cdot \mathbf{c}) \mathbf{b}-(\mathbf{a} \cdot \mathbf{b}) \mathbf{c}+(\mathbf{a} \cdot \mathbf{b}) \mathbf{b}$ $=(4-2 \beta-\sin \alpha) \mathbf{b}+\left(\beta^2-1\right) \mathbf{c}$, then $\sin (\alpha+\beta)=$

A
0
B
1
C
$\sin 1$
D
$\cos 1$
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