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 2 Offline
MCQ (More than One Correct Answer)
+4
-1
If the straight lines $$\,{{x - 1} \over 2} = {{y + 1} \over k} = {z \over 2}$$ and $${{x + 1} \over 5} = {{y + 1} \over 2} = {z \over k}$$ are coplanar, then the plane (s) containing these two lines is (are)
A
$$y+2z=-1$$
B
$$y+z=-1$$
C
$$y-z=-1$$
D
$$y-2z=-1$$
4
IIT-JEE 2012 Paper 2 Offline
+3
-1

If P is a 3 $$\times$$ 3 matrix such that PT = 2P + I, where PT is the transpose of P and I is the 3 $$\times$$ 3 identity matrix, then there exists a column matrix $$X = \left[ {\matrix{ x \cr y \cr z \cr } } \right] \ne \left[ {\matrix{ 0 \cr 0 \cr 0 \cr } } \right]$$ such that

A
$$PX = \left[ {\matrix{ 0 \cr 0 \cr 0 \cr } } \right]$$
B
PX = X
C
PX = 2X
D
PX = $$-$$X
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