1
WB JEE 2023
MCQ (Single Correct Answer)
+2
-0.5
Change Language

If the volume of the parallelopiped with $$\overrightarrow a \times \overrightarrow b ,\overrightarrow b \times \overrightarrow c $$ and $$\overrightarrow c \times \overrightarrow a $$ as conterminous edges is 9 cu. units, then the volume of the parallelopiped with $$(\overrightarrow a \times \overrightarrow b ) \times (\overrightarrow b \times \overrightarrow c ),(\overrightarrow b \times \overrightarrow c ) \times (\overrightarrow c \times \overrightarrow a )$$, and $$(\overrightarrow c \times \overrightarrow a ) \times (\overrightarrow a \times \overrightarrow b )$$ as conterminous edges is

A
9 cu. units
B
729 cu. units
C
81 cu. units
D
243 cu. units
2
WB JEE 2022
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $$\overrightarrow a = \widehat i + \widehat j - \widehat k$$, $$\overrightarrow b = \widehat i - \widehat j + \widehat k$$ and $$\overrightarrow c $$ is unit vector perpendicular to $$\overrightarrow a $$ and coplanar with $$\overrightarrow a $$ and $$\overrightarrow b $$, then unit vector $$\overrightarrow d $$ perpendicular to both $$\overrightarrow a $$ and $$\overrightarrow c $$ is

A
$$ \pm {1 \over {\sqrt 6 }}\left( {2\widehat i - \widehat j + \widehat k} \right)$$
B
$$ \pm {1 \over {\sqrt 2 }}\left( {\widehat j + \widehat k} \right)$$
C
$$ \pm {1 \over {\sqrt 6 }}\left( {\widehat i - 2\widehat j + \widehat k} \right)$$
D
$$ \pm {1 \over {\sqrt 2 }}\left( {\widehat j - \widehat k} \right)$$
3
WB JEE 2022
MCQ (Single Correct Answer)
+2
-0.5
Change Language

If $${\overrightarrow \alpha }$$ is a unit vector, $$\overrightarrow \beta = \widehat i + \widehat j - \widehat k$$, $$\overrightarrow \gamma = \widehat i + \widehat k$$ then the maximum value of $$\left[ {\overrightarrow \alpha \overrightarrow \beta \overrightarrow \gamma } \right]$$ is

A
3
B
$$\sqrt 3 $$
C
2
D
$$\sqrt 6 $$
4
WB JEE 2021
MCQ (Single Correct Answer)
+1
-0.25
Change Language
let $$\alpha$$, $$\beta$$, $$\gamma$$ be three non-zero vectors which are pairwise non-collinear. if $$\alpha$$ + 3$$\beta$$ is collinear with $$\gamma$$ and $$\beta$$ + 2$$\gamma$$ is collinear with $$\alpha$$ then $$\alpha$$ + 3$$\beta$$ + 6$$\gamma$$ is
A
$$\gamma$$
B
0
C
$$\gamma$$ + $$\gamma$$
D
$$\alpha$$
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