1
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
2
JEE Main 2019 (Online) 11th January Morning Slot
+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
$$- 14\widehat i - 5\widehat j$$
3
JEE Main 2019 (Online) 10th January Evening Slot
+4
-1
If $$\overrightarrow \alpha$$ = $$\left( {\lambda - 2} \right)\overrightarrow a + \overrightarrow b$$  and  $$\overrightarrow \beta = \left( {4\lambda - 2} \right)\overrightarrow a + 3\overrightarrow b$$ be two given vectors $$\overrightarrow a$$ and $$\overrightarrow b$$ are non-collinear. The value of $$\lambda$$ for which vectors $$\overrightarrow \alpha$$ and $$\overrightarrow \beta$$ are collinear, is -
A
4
B
3
C
$$-$$3
D
$$-$$4
4
JEE Main 2019 (Online) 10th January Morning Slot
+4
-1
Let $$\overrightarrow a = 2\widehat i + {\lambda _1}\widehat j + 3\widehat k,\,\,$$   $$\overrightarrow b = 4\widehat i + \left( {3 - {\lambda _2}} \right)\widehat j + 6\widehat k,$$  and  $$\overrightarrow c = 3\widehat i + 6\widehat j + \left( {{\lambda _3} - 1} \right)\widehat k$$  be three vectors such that $$\overrightarrow b = 2\overrightarrow a$$ and $$\overrightarrow a$$ is perpendicular to $$\overrightarrow c$$. Then a possible value of $$\left( {{\lambda _1},{\lambda _2},{\lambda _3}} \right)$$ is :
A
(1, 5, 1)
B
(1, 3, 1)
C
$$\left( { - {1 \over 2},4,0} \right)$$
D
$$\left( {{1 \over 2},4, - 2} \right)$$
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