1
AIEEE 2008
MCQ (Single Correct Answer)
+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
$$\pi $$
2
AIEEE 2007
MCQ (Single Correct Answer)
+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 $$\theta $$
3
AIEEE 2007
MCQ (Single Correct Answer)
+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
$$1.$$
4
AIEEE 2006
MCQ (Single Correct Answer)
+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
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