1
JEE Main 2021 (Online) 22th July Evening Shift
+4
-1
Out of Syllabus
Let a vector $${\overrightarrow a }$$ be coplanar with vectors $$\overrightarrow b = 2\widehat i + \widehat j + \widehat k$$ and $$\overrightarrow c = \widehat i - \widehat j + \widehat k$$. If $${\overrightarrow a}$$ is perpendicular to $$\overrightarrow d = 3\widehat i + 2\widehat j + 6\widehat k$$, and $$\left| {\overrightarrow a } \right| = \sqrt {10}$$. Then a possible value of $$[\matrix{ {\overrightarrow a } & {\overrightarrow b } & {\overrightarrow c } \cr } ] + [\matrix{ {\overrightarrow a } & {\overrightarrow b } & {\overrightarrow d } \cr } ] + [\matrix{ {\overrightarrow a } & {\overrightarrow c } & {\overrightarrow d } \cr } ]$$ is equal to :
A
$$-$$42
B
$$-$$40
C
$$-$$29
D
$$-$$38
2
JEE Main 2021 (Online) 22th July Evening Shift
+4
-1
Out of Syllabus
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
$${\left| {3\overrightarrow a + \overrightarrow b - 2\overrightarrow c } \right|^2} = 51$$
3
JEE Main 2021 (Online) 20th July Evening Shift
+4
-1
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
$${{15} \over 2}$$
4
JEE Main 2021 (Online) 20th July Morning Shift
+4
-1
Out of Syllabus
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
$${3 \over 2}$$
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