1
IIT-JEE 2012 Paper 2 Offline
+4
-1
If $$\overrightarrow a$$ and $$\overrightarrow b$$ are vectors such that $$\left| {\overrightarrow a + \overrightarrow b } \right| = \sqrt {29}$$ and $$\,\overrightarrow a \times \left( {2\widehat i + 3\widehat j + 4\widehat k} \right) = \left( {2\widehat i + 3\widehat j + 4\widehat k} \right) \times \widehat b,$$ then a possible value of $$\left( {\overrightarrow a + \overrightarrow b } \right).\left( { - 7\widehat i + 2\widehat j + 3\widehat k} \right)$$ is
A
$$0$$
B
$$3$$
C
$$4$$
D
$$8$$
2
IIT-JEE 2012 Paper 2 Offline
+4
-1
The equation of a plane passing through the line of intersection of the planes $$x+2y+3z=2$$ and $$x-y+z=3$$ and at a distance $${2 \over {\sqrt 3 }}$$ from the point $$(3, 1, -1)$$ is
A
$$5x-11y+z=17$$
B
$$\sqrt 2 x + y = 3\sqrt 2 - 1$$
C
$$x + y + z = \sqrt 3$$
D
$$x - \sqrt 2 y = 1 - \sqrt 2$$
3
IIT-JEE 2012 Paper 1 Offline
+4
-1
The point $$P$$ is the intersection of the straight line joining the points $$Q(2, 3, 5)$$ and $$R(1, -1, 4)$$ with the plane $$5x-4y-z=1.$$ If $$S$$ is the foot of the perpendicular drawn from the point $$T(2, 1, 4)$$ to $$QR,$$ then the length of the line segment $$PS$$ is
A
$${{1 \over {\sqrt 2 }}}$$
B
$${\sqrt 2 }$$
C
$$2$$
D
$${2\sqrt 2 }$$
4
IIT-JEE 2011 Paper 1 Offline
+4
-1
Let $$\overrightarrow a = \widehat i + \widehat j + \widehat k,\,\overrightarrow b = \widehat i - \widehat j + \widehat k$$ and $$\overrightarrow c = \widehat i - \widehat j - \widehat k$$ be three vectors. A vector $$\overrightarrow v$$ in the plane of $$\overrightarrow a$$ and $$\overrightarrow b ,$$ whose projection on $$\overrightarrow c$$ is $${{1 \over {\sqrt 3 }}}$$ , is given by
A
$$\widehat i - 3\widehat j + 3\widehat k$$
B
$$-3\widehat i - 3\widehat j - \widehat k$$
C
$$3\widehat i - \widehat j + 3\widehat k$$
D
$$\widehat i + 3\widehat j - 3\widehat k$$
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