1
JEE Main 2021 (Online) 24th February Morning Slot
Numerical
+4
-1
Let three vectors $$\overrightarrow a ,\overrightarrow b$$ and $$\overrightarrow c$$ be such that $$\overrightarrow c$$ is coplanar
with $$\overrightarrow a$$ and $$\overrightarrow b$$, $$\overrightarrow a .\overrightarrow c$$ = 7 and $$\overrightarrow b$$ is perpendicular to $$\overrightarrow c$$, where
$$\overrightarrow a = - \widehat i + \widehat j + \widehat k$$ and $$\overrightarrow b = 2\widehat i + \widehat k$$ , then the
value of $$2{\left| {\overrightarrow a + \overrightarrow b + \overrightarrow c } \right|^2}$$ is _____.
2
JEE Main 2020 (Online) 6th September Evening Slot
Numerical
+4
-0
If $$\overrightarrow x$$ and $$\overrightarrow y$$ be two non-zero vectors such that $$\left| {\overrightarrow x + \overrightarrow y } \right| = \left| {\overrightarrow x } \right|$$ and $${2\overrightarrow x + \lambda \overrightarrow y }$$ is perpendicular to $${\overrightarrow y }$$, then the value of $$\lambda$$ is _________ .
3
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_____.
4
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 ___________.
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