1
JEE Main 2016 (Online) 10th April Morning Slot
+4
-1
Let ABC be a triangle whose circumcentre is at P. If the position vectors of A, B, C and P are $$\overrightarrow a ,\overrightarrow b ,\overrightarrow c$$ and $${{\overrightarrow a + \overrightarrow b + \overrightarrow c } \over 4}$$ respectively, then the position vector of the orthocentre of this triangle, is :
A
$${\overrightarrow a + \overrightarrow b + \overrightarrow c }$$
B
$$- \left( {{{\overrightarrow a + \overrightarrow b + \overrightarrow c } \over 2}} \right)$$
C
$$\overrightarrow 0$$
D
$$\left( {{{\overrightarrow a + \overrightarrow b + \overrightarrow c } \over 2}} \right)$$
2
JEE Main 2016 (Online) 9th April Morning Slot
+4
-1
In a triangle ABC, right angled at the vertex A, if the position vectors of A, B and C are respectively 3$$\widehat i$$ + $$\widehat j$$ $$-$$ $$\widehat k$$,   $$-$$$$\widehat i$$ + 3$$\widehat j$$ + p$$\widehat k$$ and 5$$\widehat i$$ + q$$\widehat j$$ $$-$$ 4$$\widehat k$$, then the point (p, q) lies on a line :
A
parallel to x-axis.
B
parallel to y-axis.
C
making an acute angle with the positive direction of x-axis.
D
making an obtuse angle with the positive direction of x-axis.
3
JEE Main 2016 (Offline)
+4
-1
Out of Syllabus
Let $$\overrightarrow a ,\overrightarrow b$$ and $$\overrightarrow c$$ be three unit vectors such that $$\overrightarrow a \times \left( {\overrightarrow b \times \overrightarrow c } \right) = {{\sqrt 3 } \over 2}\left( {\overrightarrow b + \overrightarrow c } \right).$$ If $${\overrightarrow b }$$ is not parallel to $${\overrightarrow c },$$ then the angle between $${\overrightarrow a }$$ and $${\overrightarrow b }$$ is:
A
$${{2\pi } \over 3}$$
B
$${{5\pi } \over 6}$$
C
$${{3\pi } \over 4}$$
D
$${{\pi } \over 2}$$
4
JEE Main 2015 (Offline)
+4
-1
Out of Syllabus
Let $$\overrightarrow a ,\overrightarrow b$$ and $$\overrightarrow c$$ be three non-zero vectors such that no two of them are collinear and

$$\left( {\overrightarrow a \times \overrightarrow b } \right) \times \overrightarrow c = {1 \over 3}\left| {\overrightarrow b } \right|\left| {\overrightarrow c } \right|\overrightarrow a .$$ If $$\theta$$ is the angle between vectors $$\overrightarrow b$$ and $${\overrightarrow c }$$ , then a value of sin $$\theta$$ is :
A
$${2 \over 3}$$
B
$${{ - 2\sqrt 3 } \over 3}$$
C
$${{ 2\sqrt 2 } \over 3}$$
D
$${{ - \sqrt 2 } \over 3}$$
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