1
JEE Main 2016 (Offline)
+4
-1
Out of Syllabus
Let $$\overrightarrow a ,\overrightarrow b$$ and $$\overrightarrow c$$ be three unit vectors such that $$\overrightarrow a \times \left( {\overrightarrow b \times \overrightarrow c } \right) = {{\sqrt 3 } \over 2}\left( {\overrightarrow b + \overrightarrow c } \right).$$ If $${\overrightarrow b }$$ is not parallel to $${\overrightarrow c },$$ then the angle between $${\overrightarrow a }$$ and $${\overrightarrow b }$$ is:
A
$${{2\pi } \over 3}$$
B
$${{5\pi } \over 6}$$
C
$${{3\pi } \over 4}$$
D
$${{\pi } \over 2}$$
2
JEE Main 2015 (Offline)
+4
-1
Out of Syllabus
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
$${{ - \sqrt 2 } \over 3}$$
3
JEE Main 2014 (Offline)
+4
-1
Out of Syllabus
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
$$3$$
4
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
$$\sqrt {45}$$
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