1
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
$${{\pi } \over {4}}$$
2
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
$${1 \over 2}$$($$ 3\widehat i - 9\widehat j + 5\widehat k$$)
3
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
$$\sqrt {{3 \over 2}} < r \le 3\sqrt {{3 \over 2}} $$
4
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$$\sqrt 6 $$
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