1
AIEEE 2003
+4
-1
Out of Syllabus
If $$\overrightarrow u \,,\overrightarrow v$$ and $$\overrightarrow w$$ are three non-coplanar vectors, then $$\,\left( {\overrightarrow u + \overrightarrow v - \overrightarrow w } \right).\left( {\overrightarrow u - \overrightarrow v } \right) \times \left( {\overrightarrow v - \overrightarrow w} \right)$$ equals :
A
$$3\overrightarrow u .\overrightarrow v \times \overrightarrow w$$
B
$$0$$
C
$$\overrightarrow u .\overrightarrow v \times \overrightarrow w$$
D
$$\overrightarrow u .\overrightarrow w \times \overrightarrow v$$
2
AIEEE 2002
+4
-1
If $$\left| {\overrightarrow a } \right| = 4,\left| {\overrightarrow b } \right| = 2$$ and the angle between $${\overrightarrow a }$$ and $${\overrightarrow b }$$ is $$\pi /6$$ then $${\left( {\overrightarrow a \times \overrightarrow b } \right)^2}$$ is equal to :
A
$$48$$
B
$$16$$
C
$$\overrightarrow a$$
D
none of these
3
AIEEE 2002
+4
-1
Out of Syllabus
If $$\overrightarrow a \,\,,\,\,\overrightarrow b \,\,,\,\,\overrightarrow c$$ are vectors such that $$\left[ {\overrightarrow a \,\overrightarrow b \,\overrightarrow c } \right] = 4$$ then $$\left[ {\overrightarrow a \, \times \overrightarrow b \,\,\overrightarrow b \times \,\overrightarrow c \,\,\overrightarrow c \, \times \overrightarrow a } \right] =$$
A
$$16$$
B
$$64$$
C
$$4$$
D
$$8$$
4
AIEEE 2002
+4
-1
If the vectors $\overrightarrow{\mathbf{a}}, \overrightarrow{\mathbf{b}}$ and $\overrightarrow{\mathbf{c}}$ from the sides $B C, C A$ and $A B$ respectively of a triangle $A B C$, then :
A
$\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathbf{b}}=\overrightarrow{\mathbf{b}} \cdot \overrightarrow{\mathbf{c}}=\overrightarrow{\mathbf{c}} \cdot \overrightarrow{\mathbf{b}}=0$
B
$\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}}=\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{c}}=\overrightarrow{\mathbf{c}} \times \overrightarrow{\mathbf{a}}$
C
$\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathbf{b}}=\overrightarrow{\mathbf{b}} \cdot \overrightarrow{\mathbf{c}}=\overrightarrow{\mathbf{c}} \cdot \overrightarrow{\mathbf{a}}=0$
D
$\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{c}}+\overrightarrow{\mathbf{c}} \times \overrightarrow{\mathbf{a}}=\overrightarrow{\mathbf{0}}$
EXAM MAP
Medical
NEET