1
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
2
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$$\sqrt {2}$$
3
JEE Main 2021 (Online) 26th August Morning Shift
+4
-1
Out of Syllabus
Let $$\overrightarrow a = \widehat i + \widehat j + \widehat k$$ and $$\overrightarrow b = \widehat j - \widehat k$$. If $$\overrightarrow c$$ is a vector such that $$\overrightarrow a \times \overrightarrow c = \overrightarrow b$$ and $$\overrightarrow a .\overrightarrow c = 3$$, then $$\overrightarrow a .(\overrightarrow b \times \overrightarrow c )$$ is equal to :
A
$$-$$2
B
$$-$$6
C
6
D
2
4
JEE Main 2021 (Online) 27th July Evening Shift
+4
-1
Out of Syllabus
Let $$\overrightarrow a$$, $$\overrightarrow b$$ and $$\overrightarrow c$$ be three vectors such that $$\overrightarrow a$$ = $$\overrightarrow b$$ $$\times$$ ($$\overrightarrow b$$ $$\times$$ $$\overrightarrow c$$). If magnitudes of the vectors $$\overrightarrow a$$, $$\overrightarrow b$$ and $$\overrightarrow c$$ are $$\sqrt 2$$, 1 and 2 respectively and the angle between $$\overrightarrow b$$ and $$\overrightarrow c$$ is $$\theta \left( {0 < \theta < {\pi \over 2}} \right)$$, then the value of 1 + tan$$\theta$$ is equal to :
A
$$\sqrt 3 + 1$$
B
2
C
1
D
$${{\sqrt 3 + 1} \over {\sqrt 3 }}$$
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