1
AP EAPCET 2021 - 20th August Morning Shift
MCQ (Single Correct Answer)
+1
-0

If the lines, $$\frac{x-3}{2}=\frac{y-2}{3}=\frac{z-1}{\lambda}$$ and $$\frac{x-2}{3}=\frac{y-3}{2}=\frac{z-2}{3}$$ are coplanar, then $$\sin ^{-1}(\sin \lambda)+\cos ^{-1}(\cos \lambda)$$ is equal to

A
$$8-2 \pi$$
B
$$6-\pi$$
C
$$3 \pi-8$$
D
$$4 \pi-8$$
2
AP EAPCET 2021 - 20th August Morning Shift
MCQ (Single Correct Answer)
+1
-0

If a = (1, 1, 0) and b = (1, 1, 1), then unit vector in the plane of a and b and perpendicular to a is

A
(0, 1, 0)
B
(1, $$-$$1, 0)
C
k
D
(1, 0, 1)
3
AP EAPCET 2021 - 20th August Morning Shift
MCQ (Single Correct Answer)
+1
-0

The line passing through $$(1,1,-1)$$ and parallel to the vector $$\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$$ meets the line $$\frac{x-3}{-1}=\frac{y+2}{5}=\frac{z-2}{-4}$$ at $$A$$ and the plane $$2 x-y+2 z+7=0$$ at $$B$$. Then $$A B$$ is equal to

A
$$\sqrt{6}$$
B
$$2 \sqrt{6}$$
C
$$3 \sqrt{6}$$
D
$$4 \sqrt{6}$$
4
AP EAPCET 2021 - 20th August Morning Shift
MCQ (Single Correct Answer)
+1
-0

Let $$\mathbf{a}=\hat{\mathbf{i}}$$ and $$\mathbf{b}=\hat{\mathbf{j}}$$, the point of intersection of the lines $$\mathbf{r} \times \mathbf{a}=\mathbf{b} \times \mathbf{a}$$ and $$\mathbf{r} \times \mathbf{b}=\mathbf{a} \times \mathbf{b}$$ is

A
$$\mathbf{r}=\hat{i}+\hat{j}$$
B
$$\mathbf{r}=\hat{i}-\hat{j}$$
C
$$\mathbf{r}=\hat{k}$$
D
$$\mathbf{r}=2 \hat{i}+\hat{j}$$
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