1
AIEEE 2008
+4
-1
If the straight lines $$\,\,\,\,\,$$ $$\,\,\,\,\,$$ $${{x - 1} \over k} = {{y - 2} \over 2} = {{z - 3} \over 3}$$ $$\,\,\,\,\,$$ and$$\,\,\,\,\,$$ $${{x - 2} \over 3} = {{y - 3} \over k} = {{z - 1} \over 2}$$ intersects at a point, then the integer $$k$$ is equal to
A
$$-5$$
B
$$5$$
C
$$2$$
D
$$-2$$
2
AIEEE 2007
+4
-1
If a line makes an angle of $$\pi /4$$ with the positive directions of each of $$x$$-axis and $$y$$-axis, then the angle that the line makes with the positive direction of the $$z$$-axis is :
A
$${\pi \over 4}$$
B
$${\pi \over 2}$$
C
$${\pi \over 6}$$
D
$${\pi \over 3}$$
3
AIEEE 2007
+4
-1
Out of Syllabus
If $$(2,3,5)$$ is one end of a diameter of the sphere $${x^2} + {y^2} + {z^2} - 6x - 12y - 2z + 20 = 0,$$ then the coordinates of the other end of the diameter are
A
$$(4, 3, 5)$$
B
$$(4, 3, -3)$$
C
$$(4, 9, -3)$$
D
$$(4, -3, 3)$$
4
AIEEE 2007
+4
-1
Let $$L$$ be the line of intersection of the planes $$2x+3y+z=1$$ and $$x+3y+2z=2.$$ If $$L$$ makes an angle $$\alpha$$ with the positive $$x$$-axis, then cos $$\alpha$$ equals
A
$$1$$
B
$${1 \over {\sqrt 2 }}$$
C
$${1 \over {\sqrt 3 }}$$
D
$${1 \over 2}$$
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