1
IIT-JEE 2000 Screening
+4
-1
If the vectors $$\overrightarrow a ,\overrightarrow b$$ and $$\overrightarrow c$$ form the sides $$BC,$$ $$CA$$ and $$AB$$ respectively of a triangle $$ABC,$$ then
A
$$\overrightarrow a .\overrightarrow b + \overrightarrow b .\overrightarrow c + \overrightarrow c .\overrightarrow a = 0$$
B
$$\overrightarrow a \times \overrightarrow b = \overrightarrow b \times \overrightarrow c = \overrightarrow c \times \overrightarrow a$$
C
$$\overrightarrow a .\overrightarrow b = \overrightarrow b .\overrightarrow c = \overrightarrow c .\overrightarrow a$$
D
$$\overrightarrow a \times \overrightarrow b + \overrightarrow b \times \overrightarrow c + \overrightarrow c \times \overrightarrow a = \overrightarrow 0$$
2
IIT-JEE 2000 Screening
+4
-1
Let the vectors $$\overrightarrow a ,\overrightarrow b ,\overrightarrow c$$ and $$\overrightarrow d$$ be such that
$$\left( {\overrightarrow a \times \overrightarrow b } \right) \times \left( {\overrightarrow c \times \overrightarrow d } \right) = 0.$$ Let $${P_1}$$ and $${P_2}$$ be planes determined
by the pairs of vectors $$\overrightarrow a .\overrightarrow b$$ and $$\overrightarrow c .\overrightarrow d$$ respectively. Then the angle between $${P_1}$$ and $${P_2}$$ is
A
$$0$$
B
$${\pi \over 4}$$
C
$${\pi \over 3}$$
D
$${\pi \over 2}$$
3
IIT-JEE 2000 Screening
+4
-1
If $$\overrightarrow a \,,\,\overrightarrow b$$ and $$\overrightarrow c$$ are unit coplanar vectors, then the scalar triple product $$\left[ {2\overrightarrow a - \overrightarrow b ,2\overrightarrow b - \overrightarrow c ,2\overrightarrow c - \overrightarrow a } \right] =$$
A
$$0$$
B
$$1$$
C
$$- \sqrt 3$$
D
$$\sqrt 3$$
4
IIT-JEE 1999
+2
-0.5
Let $$a=2i+j-2k$$ and $$b=i+j.$$ If $$c$$ is a vector such that $$a.$$ $$c = \left| c \right|,\left| {c - a} \right| = 2\sqrt 2$$ and the angle between $$\left( {a \times b} \right)$$ and $$c$$ is $${30^ \circ },$$ then $$\left| {\left( {a \times b} \right) \times c} \right| =$$
A
$$2/3$$
B
$$3/2$$
C
$$2$$
D
$$3$$
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