1
JEE Main 2014 (Offline)
+4
-1
Out of Syllabus
If $$\left[ {\overrightarrow a \times \overrightarrow b \,\,\,\,\overrightarrow b \times \overrightarrow c \,\,\,\,\overrightarrow c \times \overrightarrow a } \right] = \lambda {\left[ {\overrightarrow a\,\,\,\,\,\,\,\, \overrightarrow b \,\,\,\,\,\,\,\,\overrightarrow c } \right]^2}$$ then $$\lambda$$ is equal to :
A
$$0$$
B
$$1$$
C
$$2$$
D
$$3$$
2
JEE Main 2013 (Offline)
+4
-1
If the vectors $$\overrightarrow {AB} = 3\widehat i + 4\widehat k$$ and $$\overrightarrow {AC} = 5\widehat i - 2\widehat j + 4\widehat k$$ are the sides of a triangle $$ABC,$$ then the length of the median through $$A$$ is :
A
$$\sqrt {18}$$
B
$$\sqrt {72}$$
C
$$\sqrt {33}$$
D
$$\sqrt {45}$$
3
AIEEE 2012
+4
-1
Let $$\overrightarrow a$$ and $$\overrightarrow b$$ be two unit vectors. If the vectors $$\,\overrightarrow c = \widehat a + 2\widehat b$$ and $$\overrightarrow d = 5\widehat a - 4\widehat b$$ are perpendicular to each other, then the angle between $$\overrightarrow a$$ and $$\overrightarrow b$$ is :
A
$${\pi \over 6}$$
B
$${\pi \over 2}$$
C
$${\pi \over 3}$$
D
$${\pi \over 4}$$
4
AIEEE 2012
+4
-1
Let $$ABCD$$ be a parallelogram such that $$\overrightarrow {AB} = \overrightarrow q ,\overrightarrow {AD} = \overrightarrow p$$ and $$\angle BAD$$ be an acute angle. If $$\overrightarrow r$$ is the vector that coincide with the altitude directed from the vertex $$B$$ to the side $$AD,$$ then $$\overrightarrow r$$ is given by :
A
$$\overrightarrow r = 3\overrightarrow q - {{3\left( {\overrightarrow p .\overrightarrow q } \right)} \over {\left( {\overrightarrow p .\overrightarrow p } \right)}}\overrightarrow p$$
B
$$\overrightarrow r = - \overrightarrow q + {{\left( {\overrightarrow p .\overrightarrow q } \right)} \over {\left( {\overrightarrow p .\overrightarrow p } \right)}}\overrightarrow p$$
C
$$\vec r = \vec q - {{\left( {\vec p.\vec q} \right)} \over {\left( {\vec p.\vec p} \right)}}\vec p$$
D
$$\overrightarrow r = - 3\overrightarrow q - {{3\left( {\overrightarrow p .\overrightarrow q } \right)} \over {\left( {\overrightarrow p .\overrightarrow p } \right)}}$$
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