1
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
$$2(\widehat i + \widehat j + \widehat k)$$
2
JEE Main 2021 (Online) 20th July Evening Shift
+4
-1
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 :
A
$${\sin ^{ - 1}}\left( {{{n - 1} \over {n + 1}}} \right)$$
B
$${\cos ^{ - 1}}\left( {{{n - 1} \over {n + 1}}} \right)$$
C
$${\sin ^{ - 1}}\left( {{{{n^2} - 1} \over {{n^2} + 1}}} \right)$$
D
$${\cos ^{ - 1}}\left( {{{{n^2} - 1} \over {{n^2} + 1}}} \right)$$
3
JEE Main 2021 (Online) 20th July Morning Shift
+4
-1
If $$\overrightarrow A$$ and $$\overrightarrow B$$ are two vectors satisfying the relation $$\overrightarrow A$$ . $$\overrightarrow B$$ = $$\left| {\overrightarrow A \times \overrightarrow B } \right|$$. Then the value of $$\left| {\overrightarrow A - \overrightarrow B } \right|$$ will be :
A
$$\sqrt {{A^2} + {B^2} + \sqrt 2 AB}$$
B
$$\sqrt {{A^2} + {B^2}}$$
C
$$\sqrt {{A^2} + {B^2} - \sqrt 2 AB}$$
D
$$\sqrt {{A^2} + {B^2} + 2AB}$$
4
JEE Main 2021 (Online) 25th February Morning Slot
+4
-1
In an octagon ABCDEFGH of equal side, what is the sum of

$$\overrightarrow {AB} + \overrightarrow {AC} + \overrightarrow {AD} + \overrightarrow {AE} + \overrightarrow {AF} + \overrightarrow {AG} + \overrightarrow {AH}$$,

if, $$\overrightarrow {AO} = 2\widehat i + 3\widehat j - 4\widehat k$$

A
$$- 16\widehat i - 24\widehat j + 32\widehat k$$
B
$$16\widehat i + 24\widehat j - 32\widehat k$$
C
$$16\widehat i + 24\widehat j + 32\widehat k$$
D
$$16\widehat i - 24\widehat j + 32\widehat k$$
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