1
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
$${\cos ^{ - 1}}\left( {{2 \over 7}} \right)$$
2
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
$$\sqrt {60}$$
3
IIT-JEE 2001 Screening
+4
-1
Let $$\overrightarrow a = \overrightarrow i - \overrightarrow k ,\overrightarrow b = x\overrightarrow i + \overrightarrow j + \left( {1 - x} \right)\overrightarrow k$$ and
$$\overrightarrow c = y\overrightarrow i - x\overrightarrow j + \left( {1 + x - y} \right)\overrightarrow k .$$ Then $$\left[ {\overrightarrow a \,\overrightarrow b \,\overrightarrow c } \right]$$ depends on
A
only $$x$$
B
only $$y$$
C
Neither $$x$$ Nor $$y$$
D
both $$x$$ and $$y$$
4
IIT-JEE 2001 Screening
+4
-1
If $$\overrightarrow a \,,\,\overrightarrow b$$ and $$\overrightarrow c$$ are unit vectors, then $${\left| {\overrightarrow a - \overrightarrow b } \right|^2} + {\left| {\overrightarrow b - \overrightarrow c } \right|^2} + {\left| {\overrightarrow c - \overrightarrow a } \right|^2}$$ does NOT exceed
A
$$4$$
B
$$9$$
C
$$8$$
D
$$6$$
EXAM MAP
Medical
NEET