1
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
$\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$
2
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
$6 \sqrt{2}$
3
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
A plane $\pi_1$ passing through the point $3 \hat{\mathbf{i}}-7 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$ is perpendicular to the vector $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and another plane $\pi_2$ passing through the point $2 \hat{\mathbf{i}}+7 \hat{\mathbf{k}}-8 \hat{\mathbf{k}}$ is perpendicular to the vector $3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}$. If $p_1$ and $p_2$ are the perpendicular distances from the origin to the planes $\pi_1$ and $\pi_2$ respectively, then $p_1-p_2=$
A
1
B
2
C
3
D
4
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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