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

Which of the following vector is equally inclined with the coordinate axes?

A
$$\hat{i}+2 \hat{j}+3 \hat{k}$$
B
$$2 \hat{i}-2 \hat{j}+\hat{k}$$
C
$$3 \hat{i}+3 \hat{j}-3 \hat{k}$$
D
$$4 \hat{i}+4 \hat{j}+4 \hat{k}$$
2
AP EAPCET 2021 - 19th August Evening Shift
+1
-0

If $$\hat{\mathbf{i}}+4 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$$, and $$3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$$ are position vectors of $$A, B$$ and $$C$$ respectively and if $$D$$ and $$E$$ are mid points of sides $$B C$$ and $$A C$$, then $$\mathbf{D E}$$ is equal to

A
$$\hat{i}+\hat{j}+\hat{k}$$
B
$$\hat{i}+\hat{j}$$
C
$$\hat{j}$$
D
$$\hat{j}+\hat{k}$$
3
AP EAPCET 2021 - 19th August Evening Shift
+1
-0

If $$\mathbf{a}$$ and $$\mathbf{b}$$ are two vectors such that $$\frac{\mathbf{a} \cdot \mathbf{b}}{|\mathbf{a}||\mathbf{b}|} < 0$$ and $$|\mathbf{a} \cdot \mathbf{b}|=|\mathbf{a} \times \mathbf{b}|$$ then the angle between the vectors $$\mathbf{a}$$ and $$\mathbf{b}$$ is

A
$$\frac{\pi}{4}$$
B
$$\sec ^{-1}(-\sqrt{2})$$
C
$$\tan ^{-1}\left(\frac{-1}{2}\right)$$
D
$$\sin ^{-1}\left(\frac{1}{2}\right)$$
4
AP EAPCET 2021 - 19th August Evening Shift
+1
-0

Let $$\mathbf{a}, \mathbf{b}$$ and $$\mathbf{c}$$ be three-unit vectors and $$\mathbf{a} \cdot \mathbf{b}=\mathbf{a} \cdot \mathbf{c}=0$$. If the angle between $$\mathbf{b}$$ and $$\mathbf{c}$$ is $$\frac{\pi}{3}$$. Then $$[\mathbf{a b c}]^2$$ is equal to

A
$$\frac{3}{2}$$
B
$$\frac{3}{4}$$
C
$$\frac{2}{3}$$
D
$$\frac{4}{3}$$
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