1
JEE Main 2019 (Online) 8th April Evening Slot
+4
-1
Let $$\mathop a\limits^ \to = 3\mathop i\limits^ \wedge + 2\mathop j\limits^ \wedge + x\mathop k\limits^ \wedge$$ and $$\mathop b\limits^ \to = \mathop i\limits^ \wedge - \mathop j\limits^ \wedge + \mathop k\limits^ \wedge$$ , for some real x. Then $$\left| {\mathop a\limits^ \to \times \mathop b\limits^ \to } \right|$$ = r is possible if :
A
0 < r < $$\sqrt {{3 \over 2}}$$
B
$$3\sqrt {{3 \over 2}} < r < 5\sqrt {{3 \over 2}}$$
C
$$r \ge 5\sqrt {{3 \over 2}}$$
D
$$\sqrt {{3 \over 2}} < r \le 3\sqrt {{3 \over 2}}$$
2
JEE Main 2019 (Online) 12th January Evening Slot
+4
-1
Out of Syllabus
Let $$\overrightarrow a$$, $$\overrightarrow b$$ and $$\overrightarrow c$$ be three unit vectors, out of which vectors $$\overrightarrow b$$ and $$\overrightarrow c$$ are non-parallel. If $$\alpha$$ and $$\beta$$ are the angles which vector $$\overrightarrow a$$ makes with vectors $$\overrightarrow b$$ and $$\overrightarrow c$$ respectively and $$\overrightarrow a$$ $$\times$$ ($$\overrightarrow b$$ $$\times$$ $$\overrightarrow c$$) = $${1 \over 2}\overrightarrow b$$, then $$\left| {\alpha - \beta } \right|$$ is equal to :
A
90o
B
30o
C
45o
D
60o
3
JEE Main 2019 (Online) 12th January Morning Slot
+4
-1
Out of Syllabus
The sum of the distinct real values of $$\mu$$, for which the vectors, $$\mu \widehat i + \widehat j + \widehat k,$$   $$\widehat i + \mu \widehat j + \widehat k,$$   $$\widehat i + \widehat j + \mu \widehat k$$  are co-planar, is :
A
2
B
$$-$$1
C
0
D
1
4
JEE Main 2019 (Online) 11th January Evening Slot
+4
-1
Let $$\sqrt 3 \widehat i + \widehat j,$$    $$\widehat i + \sqrt 3 \widehat j$$  and   $$\beta \widehat i + \left( {1 - \beta } \right)\widehat j$$ respectively be the position vectors of the points A, B and C with respect to the origin O. If the distance of C from the bisector of the acute angle between OA and OB is $${3 \over {\sqrt 2 }}$$, then the sum of all possible values of $$\beta$$ is :
A
4
B
1
C
2
D
3
EXAM MAP
Medical
NEET