1
JEE Main 2020 (Online) 6th September Morning Slot
Numerical
+4
-0
If $$\overrightarrow a$$ and $$\overrightarrow b$$ are unit vectors, then the greatest value of

$$\sqrt 3 \left| {\overrightarrow a + \overrightarrow b } \right| + \left| {\overrightarrow a - \overrightarrow b } \right|$$ is_____.
2
JEE Main 2020 (Online) 5th September Evening Slot
Numerical
+4
-0
Let the vectors $$\overrightarrow a$$, $$\overrightarrow b$$, $$\overrightarrow c$$ be such that
$$\left| {\overrightarrow a } \right| = 2$$, $$\left| {\overrightarrow b } \right| = 4$$ and $$\left| {\overrightarrow c } \right| = 4$$. If the projection of
$$\overrightarrow b$$ on $$\overrightarrow a$$ is equal to the projection of $$\overrightarrow c$$ on $$\overrightarrow a$$
and $$\overrightarrow b$$ is perpendicular to $$\overrightarrow c$$, then the value of
$$\left| {\overrightarrow a + \vec b - \overrightarrow c } \right|$$ is ___________.
3
JEE Main 2020 (Online) 4th September Evening Slot
Numerical
+4
-0
If $$\overrightarrow a = 2\widehat i + \widehat j + 2\widehat k$$, then the value of

$${\left| {\widehat i \times \left( {\overrightarrow a \times \widehat i} \right)} \right|^2} + {\left| {\widehat j \times \left( {\overrightarrow a \times \widehat j} \right)} \right|^2} + {\left| {\widehat k \times \left( {\overrightarrow a \times \widehat k} \right)} \right|^2}$$ is equal to____
4
JEE Main 2020 (Online) 2nd September Evening Slot
Numerical
+4
-0
Let the position vectors of points 'A' and 'B' be
$$\widehat i + \widehat j + \widehat k$$ and $$2\widehat i + \widehat j + 3\widehat k$$, respectively. A point 'P' divides the line segment AB internally in the ratio $$\lambda$$ : 1 ( $$\lambda$$ > 0). If O is the origin and
$$\overrightarrow {OB} .\overrightarrow {OP} - 3{\left| {\overrightarrow {OA} \times \overrightarrow {OP} } \right|^2} = 6$$, then $$\lambda$$ is equal to______.