1
JEE Main 2017 (Online) 9th April Morning Slot
+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
$$3\widehat i - 3\widehat j + 9\widehat k$$
2
JEE Main 2017 (Online) 8th April Morning Slot
+4
-1 The area (in sq. units) of the parallelogram whose diagonals are along the vectors $$8\widehat i - 6\widehat j$$ and $$3\widehat i + 4\widehat j - 12\widehat k,$$ is :
A
26
B
65
C
20
D
52
3
JEE Main 2017 (Offline)
+4
-1 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
$${{25} \over 8}$$
4
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
$$\left( {{{\overrightarrow a + \overrightarrow b + \overrightarrow c } \over 2}} \right)$$
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