1
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$P$ and $Q$ are the points of trisection of the segment $A B$. If $2 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ and $4 \hat{\mathbf{i}}+\hat{\mathbf{j}}-6 \hat{\mathbf{k}}$ are the position vectors of $A$ and $B$ respectively, then the position vector of the point which divides $P Q$ in the ratio $2: 3$ is
A
$\frac{1}{15}(44 \hat{\mathbf{i}}-33 \hat{\mathbf{j}}-18 \hat{\mathbf{k}})$
B
$\frac{1}{5}(36 \hat{\mathbf{i}}-26 \hat{\mathbf{j}}-18 \hat{\mathbf{k}})$
C
$\frac{1}{5}(3 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}-9 \hat{\mathbf{k}})$
D
$\frac{1}{15}(-3 \hat{\mathbf{i}}-7 \hat{\mathbf{j}}+9 \hat{\mathbf{k}})$
2
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The position vector of the point of intersection of the line joining the points $\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and the line joining the points $2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-6 \hat{\mathbf{k}}, 3 \hat{\mathbf{i}}-\hat{\mathbf{j}}-7 \hat{\mathbf{k}}$ is
A
$\hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$
B
$4 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}-8 \hat{\mathbf{k}}$
C
$\hat{\mathbf{i}}+3 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}$
D
$\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$
3
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\mathbf{a}=4 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ and $\mathbf{b}=6 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ are two vectors, then the magnitude of the component of $\mathbf{b}$ parallel to $\mathbf{a}$ is
A
$2 \sqrt{2}$
B
$10 \sqrt{2}$
C
$4 \sqrt{2}$
D
$6 \sqrt{2}$
4
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\mathbf{a}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}, \mathbf{b}=2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$ and $\mathbf{c}=2 \hat{\mathbf{k}}-\hat{\mathbf{i}}$ are three vectors and $\mathbf{d}$ is a unit vector perpendicular to $\mathbf{c}$. If $\mathbf{a}, \mathbf{b}$ and $\mathbf{d}$ are coplanar vectors, then $|\mathbf{d} \cdot \mathbf{b}|=$
A
0
B
$\frac{1}{\sqrt{14}}$
C
$\sqrt{\frac{2}{7}}$
D
$\sqrt{\frac{7}{2}}$
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