1
JEE Main 2018 (Online) 16th April Morning Slot
+4
-1
Let $$\overrightarrow a = \widehat i + \widehat j + \widehat k,\overrightarrow c = \widehat j - \widehat k$$ and a vector $$\overrightarrow b$$ be such that $$\overrightarrow a \times \overrightarrow b = \overrightarrow c$$ and $$\overrightarrow a .\overrightarrow b = 3.$$ Then $$\left| {\overrightarrow b } \right|$$ equals :
A
$${{11} \over 3}$$
B
$${{11} \over {\sqrt 3 }}$$
C
$$\sqrt {{{11} \over 3}}$$
D
$${{\sqrt {11} } \over 3}$$
2
JEE Main 2018 (Offline)
+4
-1
Let $$\overrightarrow u$$ be a vector coplanar with the vectors $$\overrightarrow a = 2\widehat i + 3\widehat j - \widehat k$$ and $$\overrightarrow b = \widehat j + \widehat k$$. If $$\overrightarrow u$$ is perpendicular to $$\overrightarrow a$$ and $$\overrightarrow u .\overrightarrow b = 24$$, then $${\left| {\overrightarrow u } \right|^2}$$ is equal to
A
336
B
315
C
256
D
84
3
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
If the position vectors of the vertices A, B and C of a $$\Delta$$ ABC are respectively $$4\widehat i + 7\widehat j + 8\widehat k,$$    $$2\widehat i + 3\widehat j + 4\widehat k,$$ and $$2\widehat i + 5\widehat j + 7\widehat k,$$ then the position vectors of the point, where the bisector of $$\angle$$A meets BC is :
A
$${1 \over 2}\left( {4\widehat i + 8\widehat j + 11\widehat k} \right)$$
B
$${1 \over 3}\left( {6\widehat i + 11\widehat j + 15\widehat k} \right)$$
C
$${1 \over 3}\left( {6\widehat i + 13\widehat j + 18\widehat k} \right)$$
D
$${1 \over 4}\left( {8\widehat i + 14\widehat j + 19\widehat k} \right)$$
4
JEE Main 2018 (Online) 15th April Morning Slot
+4
-1
If $$\overrightarrow a ,\,\,\overrightarrow b ,$$ and $$\overrightarrow C$$ are unit vectors such that $$\overrightarrow a + 2\overrightarrow b + 2\overrightarrow c = \overrightarrow 0 ,$$ then $$\left| {\overrightarrow a \times \overrightarrow c } \right|$$ is equal to :
A
$${{\sqrt {15} } \over 4}$$
B
$${{1} \over {4}}$$
C
$${{15} \over {16}}$$
D
$${{\sqrt {15} } \over 16}$$
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