1
JEE Main 2023 (Online) 24th January Evening Shift
+4
-1 If two vectors $$\overrightarrow P = \widehat i + 2m\widehat j + m\widehat k$$ and $$\overrightarrow Q = 4\widehat i - 2\widehat j + m\widehat k$$ are perpendicular to each other. Then, the value of m will be :

A
$$-1$$
B
3
C
1
D
2
2
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
$${\cos ^{ - 1}}\left( {{1 \over 3}} \right)$$
3
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
$$\overrightarrow A \times \overrightarrow A > 0$$
4
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
$$|\widehat A - \widehat B| = |\widehat A + \widehat B|\cos {\theta \over 2}$$
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