1
AIEEE 2004
MCQ (Single Correct Answer)
+4
-1
Let $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $$ be non-zero vectors such that $$\left( {\overrightarrow a \times \overrightarrow b } \right) \times \overrightarrow c = {1 \over 3}\left| {\overrightarrow b } \right|\left| {\overrightarrow c } \right|\overrightarrow a \,\,.$$ If $$\theta $$ is the acute angle between the vectors $${\overrightarrow b }$$ and $${\overrightarrow c },$$ then $$sin\theta $$ equals :
A
$${{2\sqrt 2 } \over 3}$$
B
$${{\sqrt 2 } \over 3}$$
C
$${2 \over 3}$$
D
$${1 \over 3}$$
2
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
If $$\overrightarrow a \times \overrightarrow b = \overrightarrow b \times \overrightarrow c = \overrightarrow c \times \overrightarrow a $$ then $$\overrightarrow a + \overrightarrow b + \overrightarrow c = $$
A
$$abc$$
B
$$-1$$
C
$$0$$
D
$$2$$
3
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
Let $$\overrightarrow u = \widehat i + \widehat j,\,\overrightarrow v = \widehat i - \widehat j$$ and $$\overrightarrow w = \widehat i + 2\widehat j + 3\widehat k\,\,.$$ If $$\widehat n$$ is a unit vector such that $$\overrightarrow u .\widehat n = 0$$ and $$\overrightarrow v .\widehat n = 0\,\,,$$ then $$\left| {\overrightarrow w .\widehat n} \right|$$ is equal to :
A
$$3$$
B
$$0$$
C
$$1$$
D
$$2$$
4
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
The vectors $$\overrightarrow {AB} = 3\widehat i + 4\widehat k\,\,\& \,\,\overrightarrow {AC} = 5\widehat i - 2\widehat j + 4\widehat k$$ are the sides of triangle $$ABC.$$ The length of the median through $$A$$ is :
A
$$\sqrt {288} $$
B
$$\sqrt {18} $$
C
$$\sqrt {72} $$
D
$$\sqrt {33} $$
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