1
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

Let $$\mathbf{a}=x \hat{i}+y \hat{j}+z \hat{k}$$ and $$x=2 y$$. If $$|\mathbf{a}|=5 \sqrt{2}$$ and a makes an angle of $$135^{\circ}$$ with the Z-axis, then $$\mathbf{a}=$$

A
$$2 \sqrt{3} \hat{i}+\sqrt{3} \hat{j}-3 \hat{k}$$
B
$$2 \sqrt{6} \hat{i}+\sqrt{6} \hat{j}-6 \hat{k}$$
C
$$2 \sqrt{5} \hat{i}+\sqrt{5} \hat{j}-5 \hat{k}$$
D
$$2 \sqrt{5} \hat{i}+\sqrt{5} \hat{j}+5 \hat{k}$$
2
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

Let $$\mathbf{a}, \mathbf{b}, \mathbf{c}$$ be the position vectors of the vertices of a $$\triangle A B C$$. Through the vertices, lines are drawn parallel to the sides to form the $$\Delta A^{\prime} B^{\prime} C^{\prime}$$. Then, the centroid of $$\Delta A^{\prime} B^{\prime} C^{\prime}$$ is

A
$$\frac{a+b+c}{9}$$
B
$$\frac{a+b+c}{6}$$
C
$$\frac{a+b+c}{3}$$
D
$$\frac{2(a+b+c)}{3}$$
3
AP EAPCET 2021 - 20th August Morning Shift
+1
-0

The position vectors of the points $$A$$ and $$B$$ with respect to $$O$$ are $$2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$$. The length of the internal bisector of $$\angle B O A$$ of $$\triangle A O B$$ is (take proportionality constant is 2)

A
$$\frac{\sqrt{136}}{9}$$
B
$$\frac{\sqrt{136}}{3}$$
C
$$\frac{20}{3}$$
D
$$\frac{25}{3}$$
4
AP EAPCET 2021 - 20th August Morning Shift
+1
-0

Let $$\mathbf{u}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{v}=-3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}$$ and $$\mathbf{w}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+4 \hat{\mathbf{k}}$$. Then which of the following statement is true?

A
$$u$$ is perpendicular to $$v$$ but not $$w$$
B
$$v$$ is perpendicular to $$w$$ but not $$u$$
C
$$w$$ is perpendicular to $$u$$ but not $$v$$
D
$$u$$ is perpendicular to both $$v$$ and $$w$$
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