1
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 $$(p,q)$$
2
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
$$\alpha = 1,\,\,\beta = 1$$
3
AIEEE 2008
+4
-1
The non-zero vectors are $${\overrightarrow a ,\overrightarrow b }$$ and $${\overrightarrow c }$$ are related by $${\overrightarrow a = 8\overrightarrow b }$$ and $${\overrightarrow c = - 7\overrightarrow b \,\,.}$$ Then the angle between $${\overrightarrow a }$$ and $${\overrightarrow c }$$ is :
A
$$0$$
B
$${\pi \over 4}$$
C
$${\pi \over 2}$$
D
$$\pi$$
4
AIEEE 2007
+4
-1
If $$\widehat u$$ and $$\widehat v$$ are unit vectors and $$\theta$$ is the acute angle between them, then $$2\widehat u \times 3\widehat v$$ is a unit vector for :
A
no value of $$\theta$$
B
exactly one value of $$\theta$$
C
exactly two values of $$\theta$$
D
more than two values of $$\theta$$
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