1
JEE Main 2018 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
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
2
JEE Main 2018 (Online) 15th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
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
$${1 \over 4}\left( {8\widehat i + 14\widehat j + 19\widehat k} \right)$$
3
JEE Main 2018 (Online) 15th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
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
$${{\sqrt {15} } \over 16}$$
4
JEE Main 2017 (Online) 9th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
If the vector $$\overrightarrow b = 3\widehat j + 4\widehat k$$ is written as the sum of a vector $$\overrightarrow {{b_1}} ,$$ paralel to $$\overrightarrow a = \widehat i + \widehat j$$ and a vector $$\overrightarrow {{b_2}} ,$$ perpendicular to $$\overrightarrow a ,$$ then $$\overrightarrow {{b_1}} \times \overrightarrow {{b_2}} $$ is equal to :
A
$$ - 3\widehat i + 3\widehat j - 9\widehat k$$
B
$$6\widehat i - 6\widehat j + {9 \over 2}\widehat k$$
C
$$ - 6\widehat i + 6\widehat j - {9 \over 2}\widehat k$$
D
$$3\widehat i - 3\widehat j + 9\widehat k$$
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