1
JEE Main 2019 (Online) 10th January Evening Slot
+4
-1
Two vectors $$\overrightarrow A$$ and $$\overrightarrow B$$ have equal magnitudes. The magnitude of $$\left( {\overrightarrow A + \overrightarrow B } \right)$$ is 'n' times the magnitude of $$\left( {\overrightarrow A - \overrightarrow B } \right)$$ . The angle between $${\overrightarrow A }$$ and $${\overrightarrow B }$$ is -
A
$${\sin ^{ - 1}}\left[ {{{n - 1} \over {n + 1}}} \right]$$
B
$${\sin ^{ - 1}}\left[ {{{{n^2} - 1} \over {{n^2} + 1}}} \right]$$
C
$${\cos ^{ - 1}}\left[ {{{{n^2} - 1} \over {{n^2} + 1}}} \right]$$
D
$${\cos ^{ - 1}}\left[ {{{n - 1} \over {n + 1}}} \right]$$
2
JEE Main 2019 (Online) 10th January Morning Slot
+4
-1
In the cube of side ‘a’ shown in the figure, the vector from the central point of the face ABOD to the central point of the face BEFO will be -

A
$${1 \over 2}a\left( {\widehat k - \widehat i} \right)$$
B
$${1 \over 2}a\left( {\widehat j - \widehat i} \right)$$
C
$${1 \over 2}a\left( {\widehat j - \widehat k} \right)$$
D
$${1 \over 2}a\left( {\widehat i - \widehat k} \right)$$
3
JEE Main 2018 (Online) 16th April Morning Slot
+4
-1
Let $$\overrightarrow A$$ = $$\left( {\widehat i + \widehat j} \right)$$ and, $$\overrightarrow B = \left( {2\widehat i - \widehat j} \right).$$ The magnitude of a coplanar vector $$\overrightarrow C$$ such that $$\overrightarrow A .\overrightarrow C = \overrightarrow B .\overrightarrow C = \overrightarrow A .\overrightarrow B ,$$ is given by :
A
$$\sqrt {{{10} \over 9}}$$
B
$$\sqrt {{{5} \over 9}}$$
C
$$\sqrt {{{20} \over 9}}$$
D
$$\sqrt {{{9} \over 12}}$$
4
AIEEE 2004
+4
-1
If $$\overrightarrow A \times \overrightarrow B = \overrightarrow B \times \overrightarrow A$$, then the angle beetween A and B is
A
$${\pi \over 2}$$
B
$${\pi \over 3}$$
C
$$\pi$$
D
$${\pi \over 4}$$
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