1
JEE Main 2021 (Online) 17th March Evening Shift
+4
-1
Let O be the origin. Let $$\overrightarrow {OP} = x\widehat i + y\widehat j - \widehat k$$ and $$\overrightarrow {OQ} = - \widehat i + 2\widehat j + 3x\widehat k$$, x, y$$\in$$R, x > 0, be such that $$\left| {\overrightarrow {PQ} } \right| = \sqrt {20}$$ and the vector $$\overrightarrow {OP}$$ is perpendicular $$\overrightarrow {OQ}$$. If $$\overrightarrow {OR}$$ = $$3\widehat i + z\widehat j - 7\widehat k$$, z$$\in$$R, is coplanar with $$\overrightarrow {OP}$$ and $$\overrightarrow {OQ}$$, then the value of x2 + y2 + z2 is equal to :
A
2
B
9
C
7
D
1
2
JEE Main 2021 (Online) 17th March Morning Shift
+4
-1
Out of Syllabus
Let $$\overrightarrow a$$ = 2$$\widehat i$$ $$-$$ 3$$\widehat j$$ + 4$$\widehat k$$ and $$\overrightarrow b$$ = 7$$\widehat i$$ + $$\widehat j$$ $$-$$ 6$$\widehat k$$.

If $$\overrightarrow r$$ $$\times$$ $$\overrightarrow a$$ = $$\overrightarrow r$$ $$\times$$ $$\overrightarrow b$$, $$\overrightarrow r$$ . ($$\widehat i$$ + 2$$\widehat j$$ + $$\widehat k$$) = $$-$$3, then $$\overrightarrow r$$ . (2$$\widehat i$$ $$-$$ 3$$\widehat j$$ + $$\widehat k$$) is equal to :
A
10
B
8
C
13
D
12
3
JEE Main 2021 (Online) 16th March Evening Shift
+4
-1
Let $$\overrightarrow a$$ = $$\widehat i$$ + 2$$\widehat j$$ $$-$$ 3$$\widehat k$$ and $$\overrightarrow b = 2\widehat i$$ $$-$$ 3$$\widehat j$$ + 5$$\widehat k$$. If $$\overrightarrow r$$ $$\times$$ $$\overrightarrow a$$ = $$\overrightarrow b$$ $$\times$$ $$\overrightarrow r$$,

$$\overrightarrow r$$ . $$\left( {\alpha \widehat i + 2\widehat j + \widehat k} \right)$$ = 3 and $$\overrightarrow r \,.\,\left( {2\widehat i + 5\widehat j - \alpha \widehat k} \right)$$ = $$-$$1, $$\alpha$$ $$\in$$ R, then the

value of $$\alpha$$ + $${\left| {\overrightarrow r } \right|^2}$$ is equal to :
A
13
B
11
C
9
D
15
4
JEE Main 2021 (Online) 16th March Morning Shift
+4
-1
Let a vector $$\alpha \widehat i + \beta \widehat j$$ be obtained by rotating the vector $$\sqrt 3 \widehat i + \widehat j$$ by an angle 45$$^\circ$$ about the origin in counterclockwise direction in the first quadrant. Then the area of triangle having vertices ($$\alpha$$, $$\beta$$), (0, $$\beta$$) and (0, 0) is equal to :
A
$${1 \over {\sqrt 2 }}$$
B
$${1 \over 2}$$
C
1
D
2$${\sqrt 2 }$$
EXAM MAP
Medical
NEET