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1
JEE Main 2021 (Online) 25th July Evening Shift
+4
-1
Two vectors $$\overrightarrow X$$ and $$\overrightarrow Y$$ have equal magnitude. The magnitude of ($$\overrightarrow X$$ $$-$$ $$\overrightarrow Y$$) is n times the magnitude of ($$\overrightarrow X$$ + $$\overrightarrow Y$$). The angle between $$\overrightarrow X$$ and $$\overrightarrow Y$$ is :
A
$${\cos ^{ - 1}}\left( {{{ - {n^2} - 1} \over {{n^2} - 1}}} \right)$$
B
$${\cos ^{ - 1}}\left( {{{{n^2} - 1} \over { - {n^2} - 1}}} \right)$$
C
$${\cos ^{ - 1}}\left( {{{{n^2} + 1} \over { - {n^2} - 1}}} \right)$$
D
$${\cos ^{ - 1}}\left( {{{{n^2} + 1} \over {{n^2} - 1}}} \right)$$
2
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
Match List - I with List - II Choose the correct answer from the options given below :
A
(a) $$\to$$ (iv), (b) $$\to$$ (i), (c) $$\to$$ (iii), (d) $$\to$$ (ii)
B
(a) $$\to$$ (iv), (b) $$\to$$ (iii), (c) $$\to$$ (i), (d) $$\to$$ (ii)
C
(a) $$\to$$ (iii), (b) $$\to$$ (ii), (c) $$\to$$ (iv), (d) $$\to$$ (i)
D
(a) $$\to$$ (i), (b) $$\to$$ (iv), (c) $$\to$$ (ii), (d) $$\to$$ (iii)
3
JEE Main 2021 (Online) 22th July Evening Shift
+4
-1
What will be the projection of vector $$\overrightarrow A = \widehat i + \widehat j + \widehat k$$ on vector $$\overrightarrow B = \widehat i + \widehat j$$ ?
A
$$\sqrt 2 (\widehat i + \widehat j + \widehat k)$$
B
$$(\widehat i + \widehat j)$$
C
$$\sqrt 2 (\widehat i + \widehat j)$$
D
$$2(\widehat i + \widehat j + \widehat k)$$
4
JEE Main 2021 (Online) 20th July Evening Shift
Two vectors $${\overrightarrow P }$$ and $${\overrightarrow Q }$$ have equal magnitudes. If the magnitude of $${\overrightarrow P + \overrightarrow Q }$$ is n times the magnitude of $${\overrightarrow P - \overrightarrow Q }$$, then angle between $${\overrightarrow P }$$ and $${\overrightarrow Q }$$ is :
$${\sin ^{ - 1}}\left( {{{n - 1} \over {n + 1}}} \right)$$
$${\cos ^{ - 1}}\left( {{{n - 1} \over {n + 1}}} \right)$$
$${\sin ^{ - 1}}\left( {{{{n^2} - 1} \over {{n^2} + 1}}} \right)$$
$${\cos ^{ - 1}}\left( {{{{n^2} - 1} \over {{n^2} + 1}}} \right)$$