1
AP EAPCET 2021 - 19th August Morning Shift
+1
-0

Angle made by the position vector of the point (5, $$-$$4, $$-$$3) with the positive direction of X-axis is

A
$$\frac{\pi}{2}$$
B
$$\frac{\pi}{6}$$
C
$$\frac{\pi}{4}$$
D
$$\frac{\pi}{3}$$
2
AP EAPCET 2021 - 19th August Morning Shift
+1
-0

If the volume of the parallelopiped formed by the vectors $$\hat{\mathbf{i}}+a \hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{j}}+a \hat{\mathbf{k}}$$ and $$a \hat{\mathbf{i}}+\hat{\mathbf{k}}$$ becomes minimum, then $$a$$ is equal to

A
$$\frac{1}{3}$$
B
$$\frac{1}{\sqrt{3}}$$
C
$$\frac{2}{\sqrt{3}}$$
D
$$\frac{2}{3}$$
3
AP EAPCET 2021 - 19th August Morning Shift
+1
-0

If $$\mathbf{a}=\frac{3}{2} \hat{\mathbf{k}}$$ and $$\mathbf{b}=\frac{2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}}{2}$$, then angle between $$\mathbf{a}+\mathbf{b}$$ and $$\mathbf{a}-\mathbf{b}$$ is

A
45$$\Upsilon$$
B
90$$\Upsilon$$
C
30$$\Upsilon$$
D
60$$\Upsilon$$
4
AP EAPCET 2021 - 19th August Morning Shift
+1
-0

Let $$\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+3 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$$ and $$\mathbf{c}=7 \hat{\mathbf{i}}+9 \hat{\mathbf{j}}+11 \hat{\mathbf{k}}$$, then the area of parallelogram having diagonals $$\mathbf{a}+\mathbf{b}$$ and $$\mathbf{b}+\mathbf{c}$$ is

A
$$4 \sqrt{6}$$ sq units
B
$$2 \sqrt{6}$$ sq units
C
$$\sqrt{6}$$ sq units
D
$$6 \sqrt{6}$$ sq units
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