1
JEE Main 2021 (Online) 26th February Morning Shift
+4
-1
If $$\overrightarrow a$$ and $$\overrightarrow b$$ are perpendicular, then
$$\overrightarrow a \times \left( {\overrightarrow a \times \left( {\overrightarrow a \times \left( {\overrightarrow a \times \overrightarrow b } \right)} \right)} \right)$$ is equal to :
A
$${1 \over 2}|\overrightarrow a {|^4}\overrightarrow b$$
B
$$\overrightarrow 0$$
C
$$\overrightarrow a \times \overrightarrow b$$
D
$$|\overrightarrow a {|^4}\overrightarrow b$$
2
JEE Main 2020 (Online) 5th September Morning Slot
+4
-1
If the volume of a parallelopiped, whose
coterminus edges are given by the
vectors $$\overrightarrow a = \widehat i + \widehat j + n\widehat k$$,
$$\overrightarrow b = 2\widehat i + 4\widehat j - n\widehat k$$ and
$$\overrightarrow c = \widehat i + n\widehat j + 3\widehat k$$ ($$n \ge 0$$), is 158 cu. units, then :
A
n = 7
B
$$\overrightarrow b .\overrightarrow c = 10$$
C
$$\overrightarrow a .\overrightarrow c = 17$$
D
n = 9
3
JEE Main 2020 (Online) 4th September Morning Slot
+4
-1
Let x0 be the point of Local maxima of $$f(x) = \overrightarrow a .\left( {\overrightarrow b \times \overrightarrow c } \right)$$, where
$$\overrightarrow a = x\widehat i - 2\widehat j + 3\widehat k$$, $$\overrightarrow b = - 2\widehat i + x\widehat j - \widehat k$$, $$\overrightarrow c = 7\widehat i - 2\widehat j + x\widehat k$$. Then the value of
$$\overrightarrow a .\overrightarrow b + \overrightarrow b .\overrightarrow c + \overrightarrow c .\overrightarrow a$$ at x = x0 is :
A
14
B
-30
C
-4
D
-22
4
JEE Main 2020 (Online) 3rd September Evening Slot
+4
-1
Let a, b c $$\in$$ R be such that a2 + b2 + c2 = 1. If
$$a\cos \theta = b\cos \left( {\theta + {{2\pi } \over 3}} \right) = c\cos \left( {\theta + {{4\pi } \over 3}} \right)$$,
where $${\theta = {\pi \over 9}}$$, then the angle between the vectors $$a\widehat i + b\widehat j + c\widehat k$$ and $$b\widehat i + c\widehat j + a\widehat k$$ is :
A
0
B
$${{\pi \over 9}}$$
C
$${{{2\pi } \over 3}}$$
D
$${{\pi \over 2}}$$
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