1
JEE Main 2019 (Online) 10th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Let A (3, 0, –1), B(2, 10, 6) and C(1, 2, 1) be the vertices of a triangle and M be the midpoint of AC. If G divides BM in the ratio, 2 : 1, then cos ($$\angle$$GOA) (O being the origin) is equal to :
A
$${1 \over {\sqrt {15} }}$$
B
$${1 \over {6\sqrt {10} }}$$
C
$${1 \over {\sqrt {30} }}$$
D
$${1 \over {2\sqrt {15} }}$$
2
JEE Main 2019 (Online) 9th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
If a unit vector $$\overrightarrow a$$ makes angles $$\pi$$/3 with $$\widehat i$$ , $$\pi$$/ 4 with $$\widehat j$$ and $$\theta$$$$\in$$(0, $$\pi$$) with $$\widehat k$$, then a value of $$\theta$$ is :-
A
$${{5\pi } \over {6}}$$
B
$${{5\pi } \over {12}}$$
C
$${{2\pi } \over {3}}$$
D
$${{\pi } \over {4}}$$
3
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
$${1 \over 2}$$($$3\widehat i - 9\widehat j + 5\widehat k$$)
4
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
$$\sqrt {{3 \over 2}} < r \le 3\sqrt {{3 \over 2}}$$
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