1
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
$$4$$
2
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
$$\sqrt 3$$
3
IIT-JEE 2002 Screening
+4
-1
If $${\overrightarrow a }$$ and $${\overrightarrow b }$$ are two unit vectors such that $${\overrightarrow a + 2\overrightarrow b }$$ and $${5\overrightarrow a - 4\overrightarrow b }$$ are perpendicular to each other then the angle between $$\overrightarrow a$$ and $$\overrightarrow b$$ is
A
$${45^ \circ }$$
B
$${60^ \circ }$$
C
$${\cos ^{ - 1}}\left( {{1 \over 3}} \right)$$
D
$${\cos ^{ - 1}}\left( {{2 \over 7}} \right)$$
4
IIT-JEE 2002 Screening
+4
-1
Let $$\overrightarrow V = 2\overrightarrow i + \overrightarrow j - \overrightarrow k$$ and $$\overrightarrow W = \overrightarrow i + 3\overrightarrow k .$$ If $$\overrightarrow U$$ is a unit vector, then the maximum value of the scalar triple product $$\left| {\overrightarrow U \overrightarrow V \overrightarrow W } \right|$$ is
A
$$-1$$
B
$$\sqrt {10} + \sqrt 6$$
C
$$\sqrt {59}$$
D
$$\sqrt {60}$$
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