1
IIT-JEE 1995 Screening
+4
-1
Let $$\overrightarrow a = \widehat i - \widehat j,\overrightarrow b = \widehat j - \widehat k,\overrightarrow c = \widehat k - \widehat i.$$ If $$\overrightarrow d$$ is a unit vector such that $$\overrightarrow a .\overrightarrow d = 0 = \left[ {\overrightarrow b \overrightarrow c \overrightarrow d } \right],$$ then $$\overrightarrow d$$ equals
A
$$\pm {{\widehat i + \widehat j - 2k} \over {\sqrt 6 }}$$
B
$$\pm {{\widehat i + \widehat j - k} \over {\sqrt 3 }}$$
C
$$\pm {{\widehat i + \widehat j + k} \over {\sqrt 3 }}$$
D
$$\pm \widehat k$$
2
IIT-JEE 1995 Screening
+4
-1
If $$\overrightarrow a ,\overrightarrow b ,\overrightarrow c$$ are non coplanar unit vectors such that $$\overrightarrow a \times \left( {\overrightarrow b \times \overrightarrow c } \right) = {{\left( {\overrightarrow b + \overrightarrow c } \right)} \over {\sqrt 2 }},\,\,$$ then the angle between $$\overrightarrow a$$ and $$\overrightarrow b$$ is
A
$${{3\pi } \over 4}$$
B
$${{\pi } \over 4}$$
C
$$\pi /2$$
D
$$\pi$$
3
IIT-JEE 1995 Screening
+4
-1
Let $$\overrightarrow u ,\overrightarrow v$$ and $$\overrightarrow w$$ be vectors such that $$\overrightarrow u + \overrightarrow v + \overrightarrow w = 0.$$ If $$\left| {\overrightarrow u } \right| = 3,\left| {\overrightarrow v } \right| = 4$$ and $$\left| {\overrightarrow w } \right| = 5,$$ then $$\overrightarrow u .\overrightarrow v + \overrightarrow v .\overrightarrow w + \overrightarrow w .\overrightarrow u$$ is
A
$$47$$
B
$$-25$$
C
$$0$$
D
$$25$$
4
IIT-JEE 1995 Screening
+4
-1
If $$\overrightarrow a ,$$ $$\overrightarrow b$$ and $$\overrightarrow c$$ are three non coplanar vectors, then
$$\left( {\overrightarrow a + \overrightarrow b + \overrightarrow c } \right).\left[ {\left( {\overrightarrow a + \overrightarrow b } \right) \times \left( {\overrightarrow a + \overrightarrow c } \right)} \right]$$ equals
A
$$0$$
B
$$\left[ {\overrightarrow a \,\overrightarrow b \,\overrightarrow c } \right]$$
C
$$2\left[ {\overrightarrow a \,\overrightarrow b \,\overrightarrow c } \right]$$
D
$$-\left[ {\overrightarrow a \,\overrightarrow b \,\overrightarrow c } \right]$$
EXAM MAP
Medical
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