1
JEE Advanced 2014 Paper 1 Offline
Numerical
+3
-0
Let $$\overrightarrow a \,\,,\,\,\overrightarrow b$$ and $$\overrightarrow c$$ be three non-coplanar unit vectors such that the angle between every pair of them is $${\pi \over 3}.$$ If $$\overrightarrow a \times \overrightarrow b + \overrightarrow b \times \overrightarrow c = p\overrightarrow a + q\overrightarrow b + r\overrightarrow c ,$$ where $$p,q$$ and $$r$$ are scalars, then the value of $${{{p^2} + 2{q^2} + {r^2}} \over {{q^2}}}$$ is
2
JEE Advanced 2013 Paper 1 Offline
Numerical
+4
-0
Consider the set of eight vectors
$$V = \left\{ {a\widehat i + b\widehat j + c\widehat k:a,b.c \in \left\{ { - 1,1} \right\}} \right\}.$$ Three non-coplanar vectors can be chosen from $$V$$ in $$2p$$ ways. Then $$p$$ is
3
IIT-JEE 2012 Paper 1 Offline
Numerical
+4
-0
If $$\overrightarrow a ,\overrightarrow b$$ and $$\overrightarrow c$$ are unit vectors satisfying
$${\left| {\overrightarrow a - \overrightarrow b } \right|^2} + {\left| {\overrightarrow b - \overrightarrow c } \right|^2} + {\left| {\overrightarrow c - \overrightarrow a } \right|^2} = 9,$$ then $$\left| {2\overrightarrow a + 5\overrightarrow b + 5\overrightarrow c } \right|$$ is
4
IIT-JEE 2011 Paper 2 Offline
Numerical
+4
-0
Let $$\overrightarrow a = - \widehat i - \widehat k,\overrightarrow b = - \widehat i + \widehat j$$ and $$\overrightarrow c = \widehat i + 2\widehat j + 3\widehat k$$ be three given vectors. If $$\overrightarrow r$$ is a vector such that $$\overrightarrow r \times \overrightarrow b = \overrightarrow c \times \overrightarrow b$$ and $$\overrightarrow r .\overrightarrow a = 0,$$ then the value of $$\overrightarrow r .\overrightarrow b$$ is