1
JEE Main 2019 (Online) 12th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
Let $$\alpha $$ $$ \in $$ R and the three vectors

$$\overrightarrow a = \alpha \widehat i + \widehat j + 3\widehat k$$, $$\overrightarrow b = 2\widehat i + \widehat j - \alpha \widehat k$$

and $$\overrightarrow c = \alpha \widehat i - 2\widehat j + 3\widehat k$$.

Then the set S = {$$\alpha $$ : $$\overrightarrow a $$ , $$\overrightarrow b $$ and $$\overrightarrow c $$ are coplanar} :
A
contains exactly two numbers only one of which is positive
B
is singleton
C
contains exactly two positive numbers
D
is empty
2
JEE Main 2019 (Online) 12th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $$\overrightarrow a = 3\widehat i + 2\widehat j + 2\widehat k$$ and $$\overrightarrow b = \widehat i + 2\widehat j - 2\widehat k$$ be two vectors. If a vector perpendicular to both the vectors $$\overrightarrow a + \overrightarrow b $$ and $$\overrightarrow a - \overrightarrow b $$ has the magnitude 12 then one such vector is :
A
$$4\left( {2\widehat i - 2\widehat j - \widehat k} \right)$$
B
$$4\left( { - 2\widehat i - 2\widehat j + \widehat k} \right)$$
C
$$4\left( {2\widehat i + 2\widehat j + \widehat k} \right)$$
D
$$4\left( {2\widehat i + 2\widehat j - \widehat k} \right)$$
3
JEE Main 2019 (Online) 12th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
If the volume of parallelopiped formed by the vectors $$\widehat i + \lambda \widehat j + \widehat k$$, $$\widehat j + \lambda \widehat k$$ and $$\lambda \widehat i + \widehat k$$ is minimum, then $$\lambda $$ is equal to :
A
$$ - {1 \over {\sqrt 3 }}$$
B
$${\sqrt 3 }$$
C
$$-{\sqrt 3 }$$
D
$$ {1 \over {\sqrt 3 }}$$
4
JEE Main 2019 (Online) 10th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
The distance of the point having position vector $$ - \widehat i + 2\widehat j + 6\widehat k$$ from the straight line passing through the point (2, 3, – 4) and parallel to the vector, $$6\widehat i + 3\widehat j - 4\widehat k$$ is :
A
6
B
7
C
$$2\sqrt {13} $$
D
$$4\sqrt 3 $$
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