1
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
$$\alpha$$
2
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
3
WB JEE 2020
+1
-0.25
The unit vector in ZOX plane, making angles $$45^\circ$$ and $$60^\circ$$ respectively with $$\alpha = 2\widehat i + 2\widehat j - \widehat k$$ and $$\beta = \widehat j - \widehat k$$ is
A
$${1 \over {\sqrt 2 }}\widehat i + {1 \over {\sqrt 2 }}\widehat j$$
B
$${1 \over {\sqrt 2 }}\widehat i - {1 \over {\sqrt 2 }}\widehat k$$
C
$${1 \over {\sqrt 2 }}\widehat i - {1 \over {\sqrt 2 }}\widehat j$$
D
$${1 \over {\sqrt 2 }}\widehat i + {1 \over {\sqrt 2 }}\widehat k$$
4
WB JEE 2019
+2
-0.5
Let $$\widehat \alpha$$, $$\widehat \beta$$, $$\widehat \gamma$$ be three unit vectors such that $$\widehat \alpha \, \times \,(\widehat \beta \times \widehat \gamma ) = {1 \over 2}(\widehat \beta + \widehat \gamma )$$ where $$\widehat \alpha \, \times \,(\widehat \beta \times \widehat \gamma ) =$$$$(\widehat \alpha \,.\,\widehat \gamma )\widehat \beta - (\widehat \alpha \,.\,\widehat \beta )\widehat \gamma$$. If $$\widehat \beta$$ is not parallel to $$\widehat \gamma$$, then the angle between $$\widehat \alpha$$ and $$\widehat \beta$$ is
A
$${{5\pi } \over 6}$$
B
$${{\pi } \over 6}$$
C
$${{\pi } \over 3}$$
D
$${{2\pi } \over 3}$$
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