1
JEE Main 2021 (Online) 26th February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If vectors $$\overrightarrow {{a_1}} = x\widehat i - \widehat j + \widehat k$$ and $$\overrightarrow {{a_2}} = \widehat i + y\widehat j + z\widehat k$$ are collinear, then a possible unit vector parallel to the vector $$x\widehat i + y\widehat j + z\widehat k$$ is :
A
$${1 \over {\sqrt 3 }}\left( {\widehat i - \widehat j + \widehat k} \right)$$
B
$${1 \over {\sqrt 2 }}\left( { - \widehat j + \widehat k} \right)$$
C
$${1 \over {\sqrt 2 }}\left( {\widehat i - \widehat j} \right)$$
D
$${1 \over {\sqrt 3 }}\left( {\widehat i + \widehat j - \widehat k} \right)$$
2
JEE Main 2021 (Online) 26th February Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
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
$$|\overrightarrow a {|^4}\overrightarrow b $$
3
JEE Main 2020 (Online) 5th September Morning Slot
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
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
4
JEE Main 2020 (Online) 4th September Morning Slot
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
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
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