1
AP EAPCET 2024 - 19th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $A(1,2,0), B(2,0,1), C(-3,0,2)$ are the vertices of $\triangle A B C$, then the length of the internal bisector of $\angle B A C$ is
A
$3 \sqrt{6}$
B
$\frac{2 \sqrt{14}}{3}$
C
$6 \sqrt{14}$
D
$\frac{2 \sqrt{6}}{3}$
2
AP EAPCET 2024 - 19th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
The perpendicular distance from the point $(-1,1,0)$ to the line joining the points $(0,2,4)$ and $(3,0,1)$ is
A
10
B
$\frac{2 \sqrt{5}}{5}$
C
$\frac{5}{\sqrt{2}}$
D
8
3
AP EAPCET 2024 - 19th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
A line $L$ passes through the points $(1,2,-3)$ and $(\beta, 3,1)$ and a plane $\pi$ passes through the points $(2,1,-2)$, $(-2,-3,6),(0,2,-1)$. If $\theta$ is the angle between the line $L$ and plane $\pi$, then $27 \cos ^2 \theta=$
A
25
B
9
C
5
D
2
4
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the points with position vectors $(\alpha \hat{\mathbf{i}}+10 \hat{\mathbf{j}}+13 \hat{\mathbf{k}}),(6 \hat{\mathbf{i}}+11 \hat{\mathbf{j}}+11 \hat{\mathbf{k}}),\left(\frac{9}{2} \hat{\mathbf{i}}+\beta \hat{\mathbf{j}}-8 \hat{\mathbf{k}}\right)$ are collinear, then $(19 \alpha-6 \beta)^2=$
A
16
B
36
C
25
D
49
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