1
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
$${\cos ^{ - 1}}\left( {{1 \over {\sqrt 3 }}} \right)$$
2
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
$${{115} \over 16}$$
3
JEE Main 2021 (Online) 18th March Morning Shift
+4
-1
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 :
A
1
B
$$- {5 \over 4}$$
C
$${4 \over 5}$$
D
$$-$$1
4
JEE Main 2021 (Online) 17th March Evening Shift
+4
-1
Let O be the origin. Let $$\overrightarrow {OP} = x\widehat i + y\widehat j - \widehat k$$ and $$\overrightarrow {OQ} = - \widehat i + 2\widehat j + 3x\widehat k$$, x, y$$\in$$R, x > 0, be such that $$\left| {\overrightarrow {PQ} } \right| = \sqrt {20}$$ and the vector $$\overrightarrow {OP}$$ is perpendicular $$\overrightarrow {OQ}$$. If $$\overrightarrow {OR}$$ = $$3\widehat i + z\widehat j - 7\widehat k$$, z$$\in$$R, is coplanar with $$\overrightarrow {OP}$$ and $$\overrightarrow {OQ}$$, then the value of x2 + y2 + z2 is equal to :
A
2
B
9
C
7
D
1
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