1
WB JEE 2023
+1
-0.25

The value of 'a' for which the scalar triple product formed by the vectors $$\overrightarrow \alpha = \widehat i + a\widehat j + \widehat k,\overrightarrow \beta = \widehat j + a\widehat k$$ and $$\overrightarrow \gamma = a\widehat i + \widehat k$$ is maximum, is

A
3
B
$$-$$3
C
$$- {1 \over {\sqrt 3 }}$$
D
$${1 \over {\sqrt 3 }}$$
2
WB JEE 2023
+2
-0.5

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
3
WB JEE 2022
+1
-0.25

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
$$\pm {1 \over {\sqrt 2 }}\left( {\widehat j - \widehat k} \right)$$
4
WB JEE 2022
+2
-0.5

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
$$\sqrt 6$$
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Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
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Calculus
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