1
JEE Main 2022 (Online) 29th June Morning Shift
+4
-1

Two vectors $$\overrightarrow A$$ and $$\overrightarrow B$$ have equal magnitudes. If magnitude of $$\overrightarrow A$$ + $$\overrightarrow B$$ is equal to two times the magnitude of $$\overrightarrow A$$ $$-$$ $$\overrightarrow B$$, then the angle between $$\overrightarrow A$$ and $$\overrightarrow B$$ will be :

A
$${\sin ^{ - 1}}\left( {{3 \over 5}} \right)$$
B
$${\sin ^{ - 1}}\left( {{1 \over 3}} \right)$$
C
$${\cos ^{ - 1}}\left( {{3 \over 5}} \right)$$
D
$${\cos ^{ - 1}}\left( {{1 \over 3}} \right)$$
2
JEE Main 2022 (Online) 25th June Morning Shift
+4
-1

$$\overrightarrow A$$ is a vector quantity such that $$|\overrightarrow A |$$ = non-zero constant. Which of the following expression is true for $$\overrightarrow A$$ ?

A
$$\overrightarrow A \,.\,\overrightarrow A = 0$$
B
$$\overrightarrow A \times \overrightarrow A < 0$$
C
$$\overrightarrow A \times \overrightarrow A = 0$$
D
$$\overrightarrow A \times \overrightarrow A > 0$$
3
JEE Main 2022 (Online) 25th June Morning Shift
+4
-1

Which of the following relations is true for two unit vector $$\widehat A$$ and $$\widehat B$$ making an angle $$\theta$$ to each other?

A
$$|\widehat A + \widehat B| = |\widehat A - \widehat B|\tan {\theta \over 2}$$
B
$$|\widehat A - \widehat B| = |\widehat A + \widehat B|\tan {\theta \over 2}$$
C
$$|\widehat A + \widehat B| = |\widehat A - \widehat B|cos{\theta \over 2}$$
D
$$|\widehat A - \widehat B| = |\widehat A + \widehat B|\cos {\theta \over 2}$$
4
JEE Main 2021 (Online) 31st August Evening Shift
+4
-1
Statement I :

Two forces $$\left( {\overrightarrow P + \overrightarrow Q } \right)$$ and $$\left( {\overrightarrow P - \overrightarrow Q } \right)$$ where $$\overrightarrow P \bot \overrightarrow Q$$, when act at an angle $$\theta$$1 to each other, the magnitude of their resultant is $$\sqrt {3({P^2} + {Q^2})}$$, when they act at an angle $$\theta$$2, the magnitude of their resultant becomes $$\sqrt {2({P^2} + {Q^2})}$$. This is possible only when $${\theta _1} < {\theta _2}$$.

Statement II :

In the situation given above.

$$\theta$$1 = 60$$^\circ$$ and $$\theta$$2 = 90$$^\circ$$

In the light of the above statements, choose the most appropriate answer from the options given below :-
A
Statement I is false but Statement II is true
B
Both Statement I and Statement II are true
C
Statement I is true but Statement II is false
D
Both Statement I and Statement II are false.
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