1
IIT-JEE 2008 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors $$\overrightarrow a \,,\,\overrightarrow b ,\overrightarrow c$$ such that $$\widehat a\,.\,\widehat b = \widehat b\,.\,\widehat c = \widehat c\,.\,\widehat a = {1 \over 2}.$$ Then, the volume of the parallelopiped is :
A
$${1 \over {\sqrt 2 }}$$
B
$${1 \over {2\sqrt 2 }}$$
C
$${{\sqrt 3 } \over 2}$$
D
$${1 \over {\sqrt 3 }}$$
2
IIT-JEE 2008 Paper 1 Offline
MCQ (Single Correct Answer)
+4
-1
Consider three planes $${P_1}:x - y + z = 1$$$$${P_2}:x + y - z = 1$$$ $${P_3}:x - 3y + 3z = 2$$\$

Let $${L_1},$$ $${L_2},$$ $${L_3}$$ be the lines of intersection of the planes $${P_2}$$ and $${P_3},$$ $${P_3}$$ and $${P_1},$$ $${P_1}$$ and $${P_2},$$ respectively.

STATEMENT - 1Z: At least two of the lines $${L_1},$$ $${L_2}$$ and $${L_3}$$ are non-parallel and

STATEMENT - 2: The three planes doe not have a common point.

A
STATEMENT - 1 is True, STATEMENT - 2 is True; STATEMENT - 2 is a correct explanation for STATEMENT - 1
B
STATEMENT - 1 is True, STATEMENT - 2 is True; STATEMENT - 2 is NOT a correct explanation for STATEMENT - 1
C
STATEMENT - 1 is True, STATEMENT - 2 is False
D
STATEMENT - 1 is False, STATEMENT - 2 is True
3
IIT-JEE 2007
MCQ (Single Correct Answer)
+3
-0.75
The minimum of distinct real values of $$\lambda ,$$ for which the vectors $$- {\lambda ^2}\widehat i + \widehat j + \widehat k,$$ $$\widehat i - {\lambda ^2}\widehat j + \widehat k$$ and $$\widehat i + \widehat j - {\lambda ^2}\widehat k$$ are coplanar, is
A
zero
B
one
C
two
D
three
4
IIT-JEE 2007
MCQ (Single Correct Answer)
+3
-0.75
Let $$\overrightarrow a \,,\,\overrightarrow b ,\overrightarrow c$$ be unit vectors such that $${\overrightarrow a + \overrightarrow b + \overrightarrow c = \overrightarrow 0 .}$$ Which one of the following is correct ?
A
$$\overrightarrow a \times \overrightarrow b = b \times \overrightarrow c = \overrightarrow c \times \overrightarrow a = \overrightarrow 0$$
B
$$\overrightarrow a \times \overrightarrow b = b \times \overrightarrow c = \overrightarrow c \times \overrightarrow a \ne \overrightarrow 0$$
C
$$\overrightarrow a \times \overrightarrow b = b \times \overrightarrow c = \overrightarrow a \times \overrightarrow c \ne \overrightarrow 0$$
D
$$\overrightarrow a \times \overrightarrow b ,b \times \overrightarrow c ,\overrightarrow c \times \overrightarrow a$$ are muturally perpendicular
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