1
IIT-JEE 2004 Screening
+4
-1
If the lines $${{x - 1} \over 2} = {{y + 1} \over 3} = {{z - 1} \over 4}$$ and $$\,{{x - 3} \over 1} = {{y - k} \over 2} = {z \over 1}$$ intersect, then the value of $$k$$ is
A
$$3/2$$
B
$$9/2$$
C
$$-2/9$$
D
$$-3/2$$
2
IIT-JEE 2004 Screening
+4
-1
The unit vector which is orthogonal to the vector $$3\overrightarrow i + 2\overrightarrow j + 6\overrightarrow k$$ and is coplanar with the vectors $$\,2\widehat i + \widehat j + \widehat k$$ and $$\,\widehat i - \widehat j + \widehat k$$$$\,\,\,$$ is
A
$${{2\widehat i - 6\widehat j + \widehat k} \over {\sqrt {41} }}$$
B
$${{2\widehat i - 3\widehat j} \over {\sqrt {13} }}$$
C
$${{3\widehat i - \widehat k} \over {\sqrt {10} }}$$
D
$${{4\widehat i + 3\widehat j - 3\widehat k} \over {\sqrt {34} }}$$
3
IIT-JEE 2003 Screening
+4
-1
The value of $$k$$ such that $${{x - 4} \over 1} = {{y - 2} \over 1} = {{z - k} \over 2}$$ lies in the plane $$2x -4y +z = 7,$$ is
A
$$7$$
B
$$-7$$
C
no real value
D
$$4$$
4
IIT-JEE 2003 Screening
+4
-1
The value of $$'a'$$ so that the volume of parallelopiped formed by $$\widehat i + a\widehat j + \widehat k,\widehat j + a\widehat k$$ and $$a\widehat i + \widehat k$$ becomes minimum is
A
$$-3$$
B
$$3$$
C
$$1/\sqrt 3$$
D
$$\sqrt 3$$
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