1
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The orthogonal projection vector of $a=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ on $\mathbf{b}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ is
A
$-\frac{1}{6}(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})$
B
$\frac{1}{6}(-\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}})$
C
$\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$
D
$-\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$
2
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\mathbf{a}=-4 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$ and $\mathbf{b}=\sqrt{2} \hat{\mathbf{i}}-\sqrt{2} \hat{\mathbf{j}}$ are two vectors, then angle between the vectors $2 \mathbf{a}$ and $\frac{\mathbf{b}}{2}$ is
A
$30^{\circ}$
B
$135^{\circ}$
C
$90^{\circ}$
D
$0^{\circ}$
3
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
A unit vector perpendicular to the vectors $a=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$ and $\mathbf{b}=3 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ is
A
$\frac{3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}}{\sqrt{22}}$
B
$\frac{3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}}{\sqrt{22}}$
C
$\frac{3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}}{\sqrt{22}}$
D
$\frac{3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}}{\sqrt{22}}$
4
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the mean of the data $7,8,9,7,8,7, \lambda$ and 8 is 8 , then variance of the data is equal to
A
2
B
$7 / 8$
C
$9 / 8$
D
1
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