1
AP EAPCET 2024 - 21th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

    $\mathbf{a}=\alpha \hat{\mathbf{i}}+\beta \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \quad \mathbf{b}=\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and $\mathbf{c}=3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ ar linearly dependent vectors and magnitude of $ \alpha $$ \sqrt{14} $${\text {}}{ }^{}$ If $\alpha, \beta$ are integers, then $\alpha+\beta=$

A
3
B
-3
C
5
D
-5
2
AP EAPCET 2024 - 21th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\mathbf{c}$ is a vector along the bisector of the internal angle between the vectors $\mathbf{a}=4 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}$ and $\mathbf{b}=12 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$. If the magnitude of $\mathbf{c}$ is $3 \sqrt{13}$, then c=
A
$5 \hat{\mathbf{i}}-8 \hat{\mathbf{j}}+2 \sqrt{2 \hat{k}}$
B
$10 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-\hat{\mathbf{k}}$
C
$\mathbf{i}-10 \mathbf{j}+4 \mathbf{k}$
D
$2 \sqrt{2} \hat{\mathbf{i}}+5 \hat{\mathbf{j}}-\mathbf{8} \hat{\mathbf{k}}$
3
AP EAPCET 2024 - 21th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\mathbf{a}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$ are two vectors and $\mathbf{c}$ is a unit vectors lying in the plane of $\mathbf{a}$ and $\mathbf{b}$. If $\mathbf{c}$ is perpendicular to $\mathbf{b}$, then $\mathbf{c}(\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}})=$
A
0
B
5
C
$\frac{1}{\sqrt{21}}$
D
$\frac{2}{\sqrt{21}}$
4
AP EAPCET 2024 - 21th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\mathbf{a}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}, \mathbf{c}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}-\hat{\mathbf{k}}$. $\mathbf{d}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$ are four vector, then $(\mathbf{a} \times \mathbf{c}) \times(\mathbf{b} \times \mathbf{d})=$
A
$2 \hat{\mathbf{i}}+19 \hat{\mathbf{j}}-11 \hat{\mathbf{k}}$
B
$-8 \hat{\mathbf{i}}+19 \hat{\mathbf{j}}-29 \hat{\mathbf{k}}$
C
$2 \mathbf{i}+\mathbf{j}-11 \mathbf{k}$
D
$-8 \hat{\mathbf{i}}+\hat{\mathbf{j}}-29 \hat{\mathbf{k}}$
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