1
AP EAPCET 2024 - 22th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
Let $\hat{\mathbf{a}}=3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}, \hat{\mathbf{b}}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$. The projection d the sum of the vectors $\hat{\mathbf{a}}$ and $\hat{\mathbf{b}}$ on the vector perpendicular to the plance of $\hat{\mathbf{a}}$ and $\hat{\mathbf{b}}$, is
A
0
B
$4 \sqrt{2}$
C
$7 \sqrt{2}$
D
$\frac{1}{\sqrt{2}}$
2
AP EAPCET 2024 - 22th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

In $\triangle P Q R,(4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}),(2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})$ and $(3 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \mathbf{k})$are$\mathbf{}$ the position vectors of the vectices $P, Q$ and $R$ respectively then, the position vector fo the point ol intersection of the angle bisector of $P$ and $Q R$ is

A
$(6 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}+9 \hat{\mathbf{k}})$
B
$(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+3 \hat{\mathbf{k}})$
C
$(5 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-2 \hat{\mathbf{k}})$
D
$\left(\frac{5}{2} \hat{\mathbf{i}}+\frac{3}{2} \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\right)$
3
AP EAPCET 2024 - 22th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\hat{\mathbf{f}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{g}}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+3 \hat{\mathbf{k}}$, then the projection vector of $\hat{\mathrm{f}}$ on $\hat{\mathrm{g}}$ is
A
$\frac{2}{7}(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})$
B
$\frac{2}{7}(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+3 \hat{\mathbf{k}})$
C
$\frac{1}{3}(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})$
D
$\frac{1}{14}(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+3 \hat{\mathbf{k}})$
4
AP EAPCET 2024 - 22th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

    If $\theta$ is the angle between $\hat{\mathbf{f}}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ and $\hat{\mathbf{g}}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+a \hat{\mathbf{k}}$ and $\sin \theta=\sqrt{\frac{24}{28}}$, then $7 a^2+24 a=$

A
10
B
12
C
36
D
15
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