1
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
2
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 $$-1$$
3
AIEEE 2005
+4
-1
If $$C$$ is the mid point of $$AB$$ and $$P$$ is any point outside $$AB,$$ then :
A
$$\overrightarrow {PA} + \overrightarrow {PB} = 2\overrightarrow {PC}$$
B
$$\overrightarrow {PA} + \overrightarrow {PB} = \overrightarrow {PC}$$
C
$$\overrightarrow {PA} + \overrightarrow {PB} = 2\overrightarrow {PC} = \overrightarrow 0$$
D
$$\overrightarrow {PA} + \overrightarrow {PB} = \overrightarrow {PC} = \overrightarrow 0$$
4
AIEEE 2005
+4
-1
Let $$a, b$$ and $$c$$ be distinct non-negative numbers. If the vectors $$a\widehat i + a\widehat j + c\widehat k,\,\,\widehat i + \widehat k$$ and $$c\widehat i + c\widehat j + b\widehat k$$ lie in a plane, then $$c$$ is :
A
the Geometric Mean of $$a$$ and $$b$$
B
the Arithmetic Mean of $$a$$ and $$b$$
C
equal to zero
D
the Harmonic Mean of $$a$$ and $$b$$
EXAM MAP
Medical
NEET