1
JEE Main 2019 (Online) 12th January Evening Slot
MCQ (Single Correct Answer)
+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
2
JEE Main 2019 (Online) 12th January Morning Slot
MCQ (Single Correct Answer)
+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
3
JEE Main 2019 (Online) 11th January Evening Slot
MCQ (Single Correct Answer)
+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
4
JEE Main 2019 (Online) 11th January Morning Slot
MCQ (Single Correct Answer)
+4
-1
Let  $$\overrightarrow a = \widehat i + 2\widehat j + 4\widehat k,$$ $$\overrightarrow b = \widehat i + \lambda \widehat j + 4\widehat k$$ and $$\overrightarrow c = 2\widehat i + 4\widehat j + \left( {{\lambda ^2} - 1} \right)\widehat k$$ be coplanar vectors. Then the non-zero vector $$\overrightarrow a \times \overrightarrow c$$ is :
A
$$- 10\widehat i - 5\widehat j$$
B
$$- 10\widehat i + 5\widehat j$$
C
$$- 14\widehat i + 5\widehat j$$
D
$$- 14\widehat i - 5\widehat j$$
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