1
JEE Main 2022 (Online) 24th June Morning Shift
+4
-1

Let $$\widehat a$$, $$\widehat b$$ be unit vectors. If $$\overrightarrow c$$ be a vector such that the angle between $$\widehat a$$ and $$\overrightarrow c$$ is $${\pi \over {12}}$$, and $$\widehat b = \overrightarrow c + 2\left( {\overrightarrow c \times \widehat a} \right)$$, then $${\left| {6\overrightarrow c } \right|^2}$$ is equal to :

A
$$6\left( {3 - \sqrt 3 } \right)$$
B
$$3 + \sqrt 3$$
C
$$6\left( {3 + \sqrt 3 } \right)$$
D
$$6\left( {\sqrt 3 + 1} \right)$$
2
JEE Main 2021 (Online) 31st August Evening Shift
+4
-1
Let $$\overrightarrow a ,\overrightarrow b ,\overrightarrow c$$ three vectors mutually perpendicular to each other and have same magnitude. If a vector $${ \overrightarrow r }$$ satisfies.

$$\overrightarrow a \times \{ (\overrightarrow r - \overrightarrow b ) \times \overrightarrow a \} + \overrightarrow b \times \{ (\overrightarrow r - \overrightarrow c ) \times \overrightarrow b \} + \overrightarrow c \times \{ (\overrightarrow r - \overrightarrow a ) \times \overrightarrow c \} = \overrightarrow 0$$, then $$\overrightarrow r$$ is equal to :
A
$${1 \over 3}(\overrightarrow a + \overrightarrow b + \overrightarrow c )$$
B
$${1 \over 3}(2\overrightarrow a + \overrightarrow b - \overrightarrow c )$$
C
$${1 \over 2}(\overrightarrow a + \overrightarrow b + \overrightarrow c )$$
D
$${1 \over 2}(\overrightarrow a + \overrightarrow b + 2\overrightarrow c )$$
3
JEE Main 2021 (Online) 31st August Morning Shift
+4
-1
Let $$\overrightarrow a$$ and $$\overrightarrow b$$ be two vectors
such that $$\left| {2\overrightarrow a + 3\overrightarrow b } \right| = \left| {3\overrightarrow a + \overrightarrow b } \right|$$ and the angle between $$\overrightarrow a$$ and $$\overrightarrow b$$ is 60$$^\circ$$. If $${1 \over 8}\overrightarrow a$$ is a unit vector, then $$\left| {\overrightarrow b } \right|$$ is equal to :
A
4
B
6
C
5
D
8
4
JEE Main 2021 (Online) 26th August Evening Shift
+4
-1
A hall has a square floor of dimension 10 m $$\times$$ 10 m (see the figure) and vertical walls. If the angle GPH between the diagonals AG and BH is $${\cos ^{ - 1}}{1 \over 5}$$, then the height of the hall (in meters) is :

A
5
B
2$$\sqrt {10}$$
C
5$$\sqrt {3}$$
D
5$$\sqrt {2}$$
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