1
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
$$-\widehat i +\widehat j - 2\widehat k$$
2
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
$$(-3, 2)$$
3
AIEEE 2009
+4
-1
Out of Syllabus
If $$\overrightarrow u ,\overrightarrow v ,\overrightarrow w$$ are non-coplanar vectors and $$p,q$$ are real numbers, then the equality $$\left[ {3\overrightarrow u \,\,p\overrightarrow v \,\,p\overrightarrow w } \right] - \left[ {p\overrightarrow v \,\,\overrightarrow w \,\,q\overrightarrow u } \right] - \left[ {2\overrightarrow w \,\,q\overrightarrow v \,\,q\overrightarrow u } \right] = 0$$ holds for :
A
exactly two values of $$(p,q)$$
B
more than two but not all values of $$(p,q)$$
C
all values of $$(p,q)$$
D
exactly one value of $$(p,q)$$
4
AIEEE 2008
+4
-1
Out of Syllabus
The vector $$\overrightarrow a = \alpha \widehat i + 2\widehat j + \beta \widehat k$$ lies in the plane of the vectors
$$\overrightarrow b = \widehat i + \widehat j$$ and $$\overrightarrow c = \widehat j + \widehat k$$ and bisects the angle between $$\overrightarrow b$$ and $$\overrightarrow c$$.Then which one of the following gives possible values of $$\alpha$$ and $$\beta$$ ?
A
$$\alpha = 2,\,\,\beta = 2$$
B
$$\alpha = 1,\,\,\beta = 2$$
C
$$\alpha = 2,\,\,\beta = 1$$
D
$$\alpha = 1,\,\,\beta = 1$$
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