1
JEE Main 2021 (Online) 22th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
Let three vectors $$\overrightarrow a $$, $$\overrightarrow b $$ and $$\overrightarrow c $$ be such that $$\overrightarrow a \times \overrightarrow b = \overrightarrow c $$, $$\overrightarrow b \times \overrightarrow c = \overrightarrow a $$ and $$\left| {\overrightarrow a } \right| = 2$$. Then which one of the following is not true?
A
$$\overrightarrow a \times \left( {(\overrightarrow b + \overrightarrow c ) \times (\overrightarrow b \times \overrightarrow c )} \right) = \overrightarrow 0 $$
B
Projection of $$\overrightarrow a $$ on $$(\overrightarrow b \times \overrightarrow c )$$ is 2
C
$$\left[ {\matrix{ {\overrightarrow a } & {\overrightarrow b } & {\overrightarrow c } \cr } } \right] + \left[ {\matrix{ {\overrightarrow c } & {\overrightarrow a } & {\overrightarrow b } \cr } } \right] = 8$$
D
$${\left| {3\overrightarrow a + \overrightarrow b - 2\overrightarrow c } \right|^2} = 51$$
2
JEE Main 2021 (Online) 20th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
In a triangle ABC, if $$\left| {\overrightarrow {BC} } \right| = 3$$, $$\left| {\overrightarrow {CA} } \right| = 5$$ and $$\left| {\overrightarrow {BA} } \right| = 7$$, then the projection of the vector $$\overrightarrow {BA} $$ on $$\overrightarrow {BC} $$ is equal to :
A
$${{19} \over 2}$$
B
$${{13} \over 2}$$
C
$${{11} \over 2}$$
D
$${{15} \over 2}$$
3
JEE Main 2021 (Online) 20th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
Let $$\overrightarrow a = 2\widehat i + \widehat j - 2\widehat k$$ and $$\overrightarrow b = \widehat i + \widehat j$$. If $$\overrightarrow c $$ is a vector such that $$\overrightarrow a .\,\overrightarrow c = \left| {\overrightarrow c } \right|,\left| {\overrightarrow c - \overrightarrow a } \right| = 2\sqrt 2 $$ and the angle between $$(\overrightarrow a \times \overrightarrow b )$$ and $$\overrightarrow c $$ is $${\pi \over 6}$$, then the value of $$\left| {\left( {\overrightarrow a \times \overrightarrow b } \right) \times \overrightarrow c } \right|$$ is :
A
$${2 \over 3}$$
B
4
C
3
D
$${3 \over 2}$$
4
JEE Main 2021 (Online) 18th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $$\overrightarrow a $$ and $$\overrightarrow b $$ be two non-zero vectors perpendicular to each other and $$|\overrightarrow a | = |\overrightarrow b |$$. If $$|\overrightarrow a \times \overrightarrow b | = |\overrightarrow a |$$, then the angle between the vectors $$\left( {\overrightarrow a + \overrightarrow b + \left( {\overrightarrow a \times \overrightarrow b } \right)} \right)$$ and $${\overrightarrow a }$$ is equal to :
A
$${\sin ^{ - 1}}\left( {{1 \over {\sqrt 6 }}} \right)$$
B
$${\cos ^{ - 1}}\left( {{1 \over {\sqrt 2 }}} \right)$$
C
$${\sin ^{ - 1}}\left( {{1 \over {\sqrt 3 }}} \right)$$
D
$${\cos ^{ - 1}}\left( {{1 \over {\sqrt 3 }}} \right)$$
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