1
JEE Main 2015 (Offline)
+4
-1
Let $$\overrightarrow a ,\overrightarrow b$$ and $$\overrightarrow c$$ be three non-zero vectors such that no two of them are collinear and

$$\left( {\overrightarrow a \times \overrightarrow b } \right) \times \overrightarrow c = {1 \over 3}\left| {\overrightarrow b } \right|\left| {\overrightarrow c } \right|\overrightarrow a .$$ If $$\theta$$ is the angle between vectors $$\overrightarrow b$$ and $${\overrightarrow c }$$ , then a value of sin $$\theta$$ is :
A
$${2 \over 3}$$
B
$${{ - 2\sqrt 3 } \over 3}$$
C
$${{ 2\sqrt 2 } \over 3}$$
D
$${{ - \sqrt 2 } \over 3}$$
2
JEE Main 2014 (Offline)
+4
-1
If $$\left[ {\overrightarrow a \times \overrightarrow b \,\,\,\,\overrightarrow b \times \overrightarrow c \,\,\,\,\overrightarrow c \times \overrightarrow a } \right] = \lambda {\left[ {\overrightarrow a \overrightarrow b \overrightarrow c } \right]^2}$$ then $$\lambda$$ is equal to
A
$$0$$
B
$$1$$
C
$$2$$
D
$$3$$
3
JEE Main 2013 (Offline)
+4
-1
If the vectors $$\overrightarrow {AB} = 3\widehat i + 4\widehat k$$ and $$\overrightarrow {AC} = 5\widehat i - 2\widehat j + 4\widehat k$$ are the sides of a triangle $$ABC,$$ then the length of the median through $$A$$ is
A
$$\sqrt {18}$$
B
$$\sqrt {72}$$
C
$$\sqrt {33}$$
D
$$\sqrt {45}$$
4
AIEEE 2012
+4
-1
Let $$\overrightarrow a$$ and $$\overrightarrow b$$ two unit vectors. If the vectors $$\,\overrightarrow c = \widehat a + 2\widehat b$$ and $$\overrightarrow d = 5\widehat a - 4\widehat b$$ are perpendicular to each other, then the angle between $$\overrightarrow a$$ and $$\overrightarrow b$$ is :
A
$${\pi \over 6}$$
B
$${\pi \over 2}$$
C
$${\pi \over 3}$$
D
$${\pi \over 4}$$
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