1
JEE Main 2019 (Online) 9th April Morning Slot
+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
+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
+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
+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
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