1
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
$$\pm {1 \over {\sqrt 2 }}\left( {\widehat j - \widehat k} \right)$$
2
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
$$\sqrt 6$$
3
WB JEE 2021
+1
-0.25
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
$$\alpha$$
4
WB JEE 2021
+2
-0.5
If a($$\alpha$$ $$\times$$ $$\beta$$) + b($$\beta$$ $$\times$$ $$\gamma$$) + c($$\gamma$$ + $$\alpha$$) = 0, where a, b, c are non-zero scalars, then the vectors $$\alpha$$, $$\beta$$, $$\gamma$$ are
A
parallel
B
non-coplanar
C
coplanar
D
mutually perpendicular
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