1
AIEEE 2011
+4
-1
Out of Syllabus
If $$\overrightarrow a = {1 \over {\sqrt {10} }}\left( {3\widehat i + \widehat k} \right)$$ and $$\overrightarrow b = {1 \over 7}\left( {2\widehat i + 3\widehat j - 6\widehat k} \right),$$ then the value

of $$\left( {2\overrightarrow a - \overrightarrow b } \right)\left[ {\left( {\overrightarrow a \times \overrightarrow b } \right) \times \left( {\overrightarrow a + 2\overrightarrow b } \right)} \right]$$ is :
A
$$-3$$
B
$$5$$
C
$$3$$
D
$$-5$$
2
AIEEE 2011
+4
-1
Let $$\overrightarrow a$$, $$\overrightarrow b$$, $$\overrightarrow c$$ be three non-zero vectors which are pairwise non-collinear. If $\overrightarrow a+3 \overrightarrow b$ is collinear with $\overrightarrow c$ and $\overrightarrow b+2 \overrightarrow c$ is collinear with $\overrightarrow a$, then $\overrightarrow a+\overrightarrow b+6 \overrightarrow c$ is :
A
$\overrightarrow a+\overrightarrow c$
B
$\overrightarrow c$
C
$\overrightarrow a$
D
$\overrightarrow 0$
3
AIEEE 2010
+4
-1
Out of Syllabus
Let $$\overrightarrow a = \widehat j - \widehat k$$ and $$\overrightarrow c = \widehat i - \widehat j - \widehat k.$$ Then the vector $$\overrightarrow b$$ satisfying $$\overrightarrow a \times \overrightarrow b + \overrightarrow c = \overrightarrow 0$$ and $$\overrightarrow a .\overrightarrow b = 3$$ :
A
$$2\widehat i - \widehat j + 2\widehat k$$
B
$$\widehat i - \widehat j - 2\widehat k$$
C
$$\widehat i + \widehat j - 2\widehat k$$
D
$$-\widehat i +\widehat j - 2\widehat k$$
4
AIEEE 2010
+4
-1
If the vectors $$\overrightarrow a = \widehat i - \widehat j + 2\widehat k,\,\,\,\,\,\overrightarrow b = 2\widehat i + 4\widehat j + \widehat k\,\,\,$$ and $$\,\overrightarrow c = \lambda \widehat i + \widehat j + \mu \widehat k$$ are mutually orthogonal, then $$\,\left( {\lambda ,\mu } \right)$$ is equal to :
A
$$(2, -3)$$
B
$$(-2, 3)$$
C
$$(3, -2)$$
D
$$(-3, 2)$$
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