1
JEE Main 2017 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $$\overrightarrow a = 2\widehat i + \widehat j -2 \widehat k$$ and $$\overrightarrow b = \widehat i + \widehat j$$.

Let $$\overrightarrow c $$ be a vector such that $$\left| {\overrightarrow c - \overrightarrow a } \right| = 3$$,

$$\left| {\left( {\overrightarrow a \times \overrightarrow b } \right) \times \overrightarrow c } \right| = 3$$ and the angle between $$\overrightarrow c $$ and $\overrightarrow a \times \overrightarrow b$ is $$30^\circ $$.

Then $$\overrightarrow a .\overrightarrow c $$ is equal to
A
2
B
5
C
$${1 \over 8}$$
D
$${{25} \over 8}$$
2
JEE Main 2016 (Online) 10th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
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
$$\left( {{{\overrightarrow a + \overrightarrow b + \overrightarrow c } \over 2}} \right)$$
3
JEE Main 2016 (Online) 9th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
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.
4
JEE Main 2016 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
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
$${{\pi } \over 2}$$
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