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1
JEE Main 2021 (Online) 20th July Morning Shift
+4
-1
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
$${3 \over 2}$$
2
JEE Main 2021 (Online) 18th March Evening Shift
+4
-1
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
$${\cos ^{ - 1}}\left( {{1 \over {\sqrt 3 }}} \right)$$
3
JEE Main 2021 (Online) 18th March Evening Shift
+4
-1
In a triangle ABC, if $$|\overrightarrow {BC} | = 8,|\overrightarrow {CA} | = 7,|\overrightarrow {AB} | = 10$$, then the projection of the vector $$\overrightarrow {AB}$$ on $$\overrightarrow {AC}$$ is equal to :
A
$${{25} \over 4}$$
B
$${{127} \over 20}$$
C
$${{85} \over 14}$$
D
$${{115} \over 16}$$
4
JEE Main 2021 (Online) 18th March Morning Shift
A vector $$\overrightarrow a$$ has components 3p and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense. If, with respect to new system, $$\overrightarrow a$$ has components p + 1 and $$\sqrt {10}$$, then the value of p is equal to :
$$- {5 \over 4}$$
$${4 \over 5}$$
$$-$$1