1
GATE EE 2011
+1
-0.3
The two vectors $$\left[ {\matrix{ {1,} & {1,} & {1} \cr } } \right]$$ and $$\left[ {\matrix{ {1,} & {a,} & {{a^2}} \cr } } \right]$$ where $$a = {{ - 1} \over 2} + j{{\sqrt 3 } \over 2}$$ are
A
Orthonormal
B
Orthogonal
C
Parallel
D
Collinear
2
GATE EE 2010
+1
-0.3
Divergence of the $$3$$ $$-$$ dimensional radial vector field $$\overrightarrow r$$ is
A
$$3$$
B
$${1 \over r}$$
C
$$\widehat i + \widehat j + \widehat k$$
D
$$3\left( {\widehat i + \widehat j + \widehat k} \right)$$
3
GATE EE 2007
+1
-0.3
Divergence of the vector field $$v\left( {x,y,z} \right) = - \left( {x\,\cos xy + y} \right)\widehat i + \left( {y\,\cos xy} \right)\widehat j + \left[ {\left( {\sin {z^2}} \right) + {x^2} + {y^2}} \right]\widehat k\,\,$$
A
$$2z\,\cos {z^2}$$
B
$$\,\sin \,xy + 2z\,\cos {z^2}$$
C
$$x\,\sin xy - \cos z$$
D
none of these
4
GATE EE 2002
+1
-0.3
Given a vector field $${\overrightarrow F ,}$$ the divergence theorem states that
A
$$\int\limits_s {\overrightarrow F .d\overrightarrow s = \int\limits_v \nabla .\overrightarrow F \,dv}$$
B
$$\int\limits_s {\overrightarrow F .d\overrightarrow s = \int\limits_v \nabla \times \overrightarrow F \,dv}$$
C
$$\int\limits_s {\overrightarrow F \times d\overrightarrow s = \int\limits_v \nabla .\overrightarrow F \,dv}$$
D
$$\int\limits_s {\overrightarrow F \times d\overrightarrow s = \int\limits_v \nabla \times \overrightarrow F \,dv}$$
EXAM MAP
Medical
NEET