WB JEE 2022 | Vector Algebra Question 14 | Mathematics

WB JEE 2022

MCQ (Single Correct Answer)

-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

$$ \pm {1 \over {\sqrt 6 }}\left( {2\widehat i - \widehat j + \widehat k} \right)$$

$$ \pm {1 \over {\sqrt 2 }}\left( {\widehat j + \widehat k} \right)$$

$$ \pm {1 \over {\sqrt 6 }}\left( {\widehat i - 2\widehat j + \widehat k} \right)$$

$$ \pm {1 \over {\sqrt 2 }}\left( {\widehat j - \widehat k} \right)$$

WB JEE 2022

MCQ (Single Correct Answer)

-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

$$\sqrt 3 $$

$$\sqrt 6 $$

WB JEE 2021

MCQ (Single Correct Answer)

-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

$$\gamma$$

$$\gamma$$ + $$\gamma$$

$$\alpha$$

WB JEE 2021

MCQ (Single Correct Answer)

-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

parallel

non-coplanar

coplanar

mutually perpendicular

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