1
JEE Main 2019 (Online) 9th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Let $$\overrightarrow \alpha = 3\widehat i + \widehat j$$ and $$\overrightarrow \beta = 2\widehat i - \widehat j + 3 \widehat k$$ . If $$\overrightarrow \beta = {\overrightarrow \beta _1} - \overrightarrow {{\beta _2}}$$, where $${\overrightarrow \beta _1}$$ is parallel to $$\overrightarrow \alpha$$ and $$\overrightarrow {{\beta _2}}$$ is perpendicular to $$\overrightarrow \alpha$$ , then $${\overrightarrow \beta _1} \times \overrightarrow {{\beta _2}}$$ is equal to
A
$$3\widehat i - 9\widehat j - 5\widehat k$$
B
$${1 \over 2}$$($$- 3\widehat i + 9\widehat j + 5\widehat k$$)
C
$$- 3\widehat i + 9\widehat j + 5\widehat k$$
D
$${1 \over 2}$$($$3\widehat i - 9\widehat j + 5\widehat k$$)
2
JEE Main 2019 (Online) 8th April Evening Slot
MCQ (Single Correct Answer)
+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
$$\sqrt {{3 \over 2}} < r \le 3\sqrt {{3 \over 2}}$$
3
JEE Main 2019 (Online) 8th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
The magnitude of the projection of the vector $$\mathop {2i}\limits^ \wedge + \mathop {3j}\limits^ \wedge + \mathop k\limits^ \wedge$$ on the vector perpendicular to the plane containing the vectors $$\mathop {i}\limits^ \wedge + \mathop {j}\limits^ \wedge + \mathop k\limits^ \wedge$$ and $$\mathop {i}\limits^ \wedge + \mathop {2j}\limits^ \wedge + \mathop {3k}\limits^ \wedge$$ , is
A
$${{\sqrt 3 } \over 2}$$
B
$$\sqrt 6$$
C
$$\sqrt {3 \over 2}$$
D
3$$\sqrt 6$$
4
JEE Main 2019 (Online) 12th January Evening Slot
MCQ (Single Correct Answer)
+4
-1
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
JEE Main Subjects
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
EXAM MAP
Joint Entrance Examination
JEE MainJEE AdvancedWB JEE
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Medical
NEET