1
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 $$\theta$$
2
AIEEE 2007
+4
-1
Out of Syllabus
Let $$\overrightarrow a = \widehat i + \widehat j + \widehat k,\overrightarrow b = \widehat i - \widehat j + 2\widehat k$$ and $$\overrightarrow c = x\widehat i + \left( {x - 2} \right)\widehat j - \widehat k\,\,.$$ If the vectors $$\overrightarrow c$$ lies in the plane of $$\overrightarrow a$$ and $$\overrightarrow b$$, then $$x$$ equals :
A
$$-4$$
B
$$-2$$
C
$$0$$
D
$$1.$$
3
AIEEE 2006
+4
-1
Out of Syllabus
If $$\left( {\overrightarrow a \times \overrightarrow b } \right) \times \overrightarrow c = \overrightarrow a \times \left( {\overrightarrow b \times \overrightarrow c } \right)$$ where $${\overrightarrow a ,\overrightarrow b }$$ and $${\overrightarrow c }$$ are any three vectors such that $$\overrightarrow a .\overrightarrow b \ne 0,\,\,\overrightarrow b .\overrightarrow c \ne 0$$ then $${\overrightarrow a }$$ and $${\overrightarrow c }$$ are :
A
inclined at an angle of $${\pi \over 3}$$ between them
B
inclined at an angle of $${\pi \over 6}$$ between them
C
perpendicular
D
parallel
4
AIEEE 2006
+4
-1
The values of a, for which the points $$A, B, C$$ with position vectors $$2\widehat i - \widehat j + \widehat k,\,\,\widehat i - 3\widehat j - 5\widehat k$$ and $$a\widehat i - 3\widehat j + \widehat k$$ respectively are the vertices of a right angled triangle with $$C = {\pi \over 2}$$ are :
A
$$2$$ and $$1$$
B
$$-2$$ and $$-1$$
C
$$-2$$ and $$1$$
D
$$2$$ and $$-1$$
EXAM MAP
Medical
NEET